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iz(z^2+7)+6=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
    / 2    \        
I*z*\z  + 7/ + 6 = 0
iz(z2+7)+6=0i z \left(z^{2} + 7\right) + 6 = 0
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
                                                /                                                       /    /    ___\\             /    /    ___\\\            /    /    ___\\             /    /    ___\\                                                   /                                                       /    /    ___\\             /    /    ___\\\            /    /    ___\\             /    /    ___\\                 /    /    ___\\
                                                |                                                       |    |9*\/ 3 ||             |    |9*\/ 3 |||            |    |9*\/ 3 ||             |    |9*\/ 3 ||                                                   |                                                       |    |9*\/ 3 ||             |    |9*\/ 3 |||            |    |9*\/ 3 ||             |    |9*\/ 3 ||                 |    |9*\/ 3 ||
                                                |                                                       |atan|-------||             |atan|-------|||            |atan|-------||             |atan|-------||                                                   |                                                       |atan|-------||             |atan|-------|||            |atan|-------||             |atan|-------||                 |atan|-------||
                                                |                                                ___    |    \   10  /|     ____    |    \   10  /||     ___    |    \   10  /|     ____    |    \   10  /|                                                   |                                                ___    |    \   10  /|     ____    |    \   10  /||     ___    |    \   10  /|     ____    |    \   10  /|         ____    |    \   10  /|
                                                |                                              \/ 7 *cos|-------------|   \/ 21 *sin|-------------||   \/ 7 *sin|-------------|   \/ 21 *cos|-------------|                                                   |                                              \/ 7 *cos|-------------|   \/ 21 *sin|-------------||   \/ 7 *sin|-------------|   \/ 21 *cos|-------------|   2*I*\/ 21 *sin|-------------|
    /                  1                  \     |    /                  1                  \            \      3      /             \      3      /|            \      3      /             \      3      /       /                  1                  \     |    /                  1                  \            \      3      /             \      3      /|            \      3      /             \      3      /                 \      3      /
7*re|-------------------------------------| + I*|7*im|-------------------------------------| + ------------------------ - -------------------------| + ------------------------ + ------------------------- + 7*re|-------------------------------------| + I*|7*im|-------------------------------------| - ------------------------ - -------------------------| - ------------------------ + ------------------------- + -----------------------------
    |/          ___\    __________________|     |    |/          ___\    __________________|              2                           6            |              2                           6                   |/          ___\    __________________|     |    |/          ___\    __________________|              2                           6            |              2                           6                             3              
    ||  1   I*\/ 3 | 3 /              ___ |     |    ||  1   I*\/ 3 | 3 /              ___ |                                                       |                                                              ||  1   I*\/ 3 | 3 /              ___ |     |    ||  1   I*\/ 3 | 3 /              ___ |                                                       |                                                                                       
    ||- - - -------|*\/  -81*I + 30*\/ 3  |     |    ||- - - -------|*\/  -81*I + 30*\/ 3  |                                                       |                                                              ||- - + -------|*\/  -81*I + 30*\/ 3  |     |    ||- - + -------|*\/  -81*I + 30*\/ 3  |                                                       |                                                                                       
    \\  2      2   /                      /     \    \\  2      2   /                      /                                                       /                                                              \\  2      2   /                      /     \    \\  2      2   /                      /                                                       /
((−7sin⁡(atan⁡(9310)3)2+7re⁡(1(−12+3i2)303−81i3)+21cos⁡(atan⁡(9310)3)6+i(7im⁡(1(−12+3i2)303−81i3)−7cos⁡(atan⁡(9310)3)2−21sin⁡(atan⁡(9310)3)6))+(7re⁡(1(−12−3i2)303−81i3)+7sin⁡(atan⁡(9310)3)2+21cos⁡(atan⁡(9310)3)6+i(−21sin⁡(atan⁡(9310)3)6+7im⁡(1(−12−3i2)303−81i3)+7cos⁡(atan⁡(9310)3)2)))+221isin⁡(atan⁡(9310)3)3\left(\left(- \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + 7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} - \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} - \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6}\right)\right) + \left(7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(- \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + 7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2}\right)\right)\right) + \frac{2 \sqrt{21} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{3} 
=
                                                                                              /                                                       /    /    ___\\             /    /    ___\\\     /                                                       /    /    ___\\             /    /    ___\\\             /    /    ___\\                 /    /    ___\\
                                                                                              |                                                       |    |9*\/ 3 ||             |    |9*\/ 3 |||     |                                                       |    |9*\/ 3 ||             |    |9*\/ 3 |||             |    |9*\/ 3 ||                 |    |9*\/ 3 ||
                                                                                              |                                                       |atan|-------||             |atan|-------|||     |                                                       |atan|-------||             |atan|-------|||             |atan|-------||                 |atan|-------||
                                                                                              |                                                ___    |    \   10  /|     ____    |    \   10  /||     |                                                ___    |    \   10  /|     ____    |    \   10  /||     ____    |    \   10  /|         ____    |    \   10  /|
                                                                                              |                                              \/ 7 *cos|-------------|   \/ 21 *sin|-------------||     |                                              \/ 7 *cos|-------------|   \/ 21 *sin|-------------||   \/ 21 *cos|-------------|   2*I*\/ 21 *sin|-------------|
    /                  1                  \       /                  1                  \     |    /                  1                  \            \      3      /             \      3      /|     |    /                  1                  \            \      3      /             \      3      /|             \      3      /                 \      3      /
7*re|-------------------------------------| + 7*re|-------------------------------------| + I*|7*im|-------------------------------------| - ------------------------ - -------------------------| + I*|7*im|-------------------------------------| + ------------------------ - -------------------------| + ------------------------- + -----------------------------
    |/          ___\    __________________|       |/          ___\    __________________|     |    |/          ___\    __________________|              2                           6            |     |    |/          ___\    __________________|              2                           6            |               3                             3              
    ||  1   I*\/ 3 | 3 /              ___ |       ||  1   I*\/ 3 | 3 /              ___ |     |    ||  1   I*\/ 3 | 3 /              ___ |                                                       |     |    ||  1   I*\/ 3 | 3 /              ___ |                                                       |                                                            
    ||- - + -------|*\/  -81*I + 30*\/ 3  |       ||- - - -------|*\/  -81*I + 30*\/ 3  |     |    ||- - + -------|*\/  -81*I + 30*\/ 3  |                                                       |     |    ||- - - -------|*\/  -81*I + 30*\/ 3  |                                                       |                                                            
    \\  2      2   /                      /       \\  2      2   /                      /     \    \\  2      2   /                      /                                                       /     \    \\  2      2   /                      /                                                       /
7re⁡(1(−12−3i2)303−81i3)+7re⁡(1(−12+3i2)303−81i3)+21cos⁡(atan⁡(9310)3)3+i(7im⁡(1(−12+3i2)303−81i3)−7cos⁡(atan⁡(9310)3)2−21sin⁡(atan⁡(9310)3)6)+221isin⁡(atan⁡(9310)3)3+i(−21sin⁡(atan⁡(9310)3)6+7im⁡(1(−12−3i2)303−81i3)+7cos⁡(atan⁡(9310)3)2)7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + 7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{3} + i \left(7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} - \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} - \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6}\right) + \frac{2 \sqrt{21} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{3} + i \left(- \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + 7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2}\right) 
producto
/                                                /                                                       /    /    ___\\             /    /    ___\\\            /    /    ___\\             /    /    ___\\\ /                                                /                                                       /    /    ___\\             /    /    ___\\\            /    /    ___\\             /    /    ___\\\               /    /    ___\\
|                                                |                                                       |    |9*\/ 3 ||             |    |9*\/ 3 |||            |    |9*\/ 3 ||             |    |9*\/ 3 ||| |                                                |                                                       |    |9*\/ 3 ||             |    |9*\/ 3 |||            |    |9*\/ 3 ||             |    |9*\/ 3 |||               |    |9*\/ 3 ||
|                                                |                                                       |atan|-------||             |atan|-------|||            |atan|-------||             |atan|-------||| |                                                |                                                       |atan|-------||             |atan|-------|||            |atan|-------||             |atan|-------|||               |atan|-------||
|                                                |                                                ___    |    \   10  /|     ____    |    \   10  /||     ___    |    \   10  /|     ____    |    \   10  /|| |                                                |                                                ___    |    \   10  /|     ____    |    \   10  /||     ___    |    \   10  /|     ____    |    \   10  /||       ____    |    \   10  /|
|                                                |                                              \/ 7 *cos|-------------|   \/ 21 *sin|-------------||   \/ 7 *sin|-------------|   \/ 21 *cos|-------------|| |                                                |                                              \/ 7 *cos|-------------|   \/ 21 *sin|-------------||   \/ 7 *sin|-------------|   \/ 21 *cos|-------------|| 2*I*\/ 21 *sin|-------------|
|    /                  1                  \     |    /                  1                  \            \      3      /             \      3      /|            \      3      /             \      3      /| |    /                  1                  \     |    /                  1                  \            \      3      /             \      3      /|            \      3      /             \      3      /|               \      3      /
|7*re|-------------------------------------| + I*|7*im|-------------------------------------| + ------------------------ - -------------------------| + ------------------------ + -------------------------|*|7*re|-------------------------------------| + I*|7*im|-------------------------------------| - ------------------------ - -------------------------| - ------------------------ + -------------------------|*-----------------------------
|    |/          ___\    __________________|     |    |/          ___\    __________________|              2                           6            |              2                           6            | |    |/          ___\    __________________|     |    |/          ___\    __________________|              2                           6            |              2                           6            |               3              
|    ||  1   I*\/ 3 | 3 /              ___ |     |    ||  1   I*\/ 3 | 3 /              ___ |                                                       |                                                       | |    ||  1   I*\/ 3 | 3 /              ___ |     |    ||  1   I*\/ 3 | 3 /              ___ |                                                       |                                                       |                              
|    ||- - - -------|*\/  -81*I + 30*\/ 3  |     |    ||- - - -------|*\/  -81*I + 30*\/ 3  |                                                       |                                                       | |    ||- - + -------|*\/  -81*I + 30*\/ 3  |     |    ||- - + -------|*\/  -81*I + 30*\/ 3  |                                                       |                                                       |                              
\    \\  2      2   /                      /     \    \\  2      2   /                      /                                                       /                                                       / \    \\  2      2   /                      /     \    \\  2      2   /                      /                                                       /                                                       /
(−7sin⁡(atan⁡(9310)3)2+7re⁡(1(−12+3i2)303−81i3)+21cos⁡(atan⁡(9310)3)6+i(7im⁡(1(−12+3i2)303−81i3)−7cos⁡(atan⁡(9310)3)2−21sin⁡(atan⁡(9310)3)6))(7re⁡(1(−12−3i2)303−81i3)+7sin⁡(atan⁡(9310)3)2+21cos⁡(atan⁡(9310)3)6+i(−21sin⁡(atan⁡(9310)3)6+7im⁡(1(−12−3i2)303−81i3)+7cos⁡(atan⁡(9310)3)2))221isin⁡(atan⁡(9310)3)3\left(- \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + 7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} - \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} - \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6}\right)\right) \left(7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(- \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + 7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2}\right)\right) \frac{2 \sqrt{21} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{3} 
=
6*I
6i6 i 
6*i
Respuesta rápida [src] 
                                                     /                                                       /    /    ___\\             /    /    ___\\\            /    /    ___\\             /    /    ___\\
                                                     |                                                       |    |9*\/ 3 ||             |    |9*\/ 3 |||            |    |9*\/ 3 ||             |    |9*\/ 3 ||
                                                     |                                                       |atan|-------||             |atan|-------|||            |atan|-------||             |atan|-------||
                                                     |                                                ___    |    \   10  /|     ____    |    \   10  /||     ___    |    \   10  /|     ____    |    \   10  /|
                                                     |                                              \/ 7 *cos|-------------|   \/ 21 *sin|-------------||   \/ 7 *sin|-------------|   \/ 21 *cos|-------------|
         /                  1                  \     |    /                  1                  \            \      3      /             \      3      /|            \      3      /             \      3      /
z1 = 7*re|-------------------------------------| + I*|7*im|-------------------------------------| + ------------------------ - -------------------------| + ------------------------ + -------------------------
         |/          ___\    __________________|     |    |/          ___\    __________________|              2                           6            |              2                           6            
         ||  1   I*\/ 3 | 3 /              ___ |     |    ||  1   I*\/ 3 | 3 /              ___ |                                                       |                                                       
         ||- - - -------|*\/  -81*I + 30*\/ 3  |     |    ||- - - -------|*\/  -81*I + 30*\/ 3  |                                                       |                                                       
         \\  2      2   /                      /     \    \\  2      2   /                      /                                                       /
z1=7re⁡(1(−12−3i2)303−81i3)+7sin⁡(atan⁡(9310)3)2+21cos⁡(atan⁡(9310)3)6+i(−21sin⁡(atan⁡(9310)3)6+7im⁡(1(−12−3i2)303−81i3)+7cos⁡(atan⁡(9310)3)2)z_{1} = 7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(- \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + 7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2}\right) 
                                                     /                                                       /    /    ___\\             /    /    ___\\\            /    /    ___\\             /    /    ___\\
                                                     |                                                       |    |9*\/ 3 ||             |    |9*\/ 3 |||            |    |9*\/ 3 ||             |    |9*\/ 3 ||
                                                     |                                                       |atan|-------||             |atan|-------|||            |atan|-------||             |atan|-------||
                                                     |                                                ___    |    \   10  /|     ____    |    \   10  /||     ___    |    \   10  /|     ____    |    \   10  /|
                                                     |                                              \/ 7 *cos|-------------|   \/ 21 *sin|-------------||   \/ 7 *sin|-------------|   \/ 21 *cos|-------------|
         /                  1                  \     |    /                  1                  \            \      3      /             \      3      /|            \      3      /             \      3      /
z2 = 7*re|-------------------------------------| + I*|7*im|-------------------------------------| - ------------------------ - -------------------------| - ------------------------ + -------------------------
         |/          ___\    __________________|     |    |/          ___\    __________________|              2                           6            |              2                           6            
         ||  1   I*\/ 3 | 3 /              ___ |     |    ||  1   I*\/ 3 | 3 /              ___ |                                                       |                                                       
         ||- - + -------|*\/  -81*I + 30*\/ 3  |     |    ||- - + -------|*\/  -81*I + 30*\/ 3  |                                                       |                                                       
         \\  2      2   /                      /     \    \\  2      2   /                      /                                                       /
z2=−7sin⁡(atan⁡(9310)3)2+7re⁡(1(−12+3i2)303−81i3)+21cos⁡(atan⁡(9310)3)6+i(7im⁡(1(−12+3i2)303−81i3)−7cos⁡(atan⁡(9310)3)2−21sin⁡(atan⁡(9310)3)6)z_{2} = - \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + 7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} - \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} - \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6}\right) 
                   /    /    ___\\
                   |    |9*\/ 3 ||
                   |atan|-------||
           ____    |    \   10  /|
     2*I*\/ 21 *sin|-------------|
                   \      3      /
z3 = -----------------------------
                   3
z3=221isin⁡(atan⁡(9310)3)3z_{3} = \frac{2 \sqrt{21} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{3} 
z3 = 2*sqrt(21)*i*sin(atan(9*sqrt(3)/10)/3)/3
Respuesta numérica [src] 
z1 = -5.29395592033938e-23 - 3.0*i
z2 = 1.35525271560688e-20 + 2.0*i
z3 = 2.11758236813575e-22 + 1.0*i
z3 = 2.11758236813575e-22 + 1.0*i
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