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z=arcsin*(xy)^0.5 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
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z = \/ asin(x*y)
z=asin⁡(xy)z = \sqrt{\operatorname{asin}{\left(x y \right)}}
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Gráfica
Suma y producto de raíces [src] 
suma
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4 /   2                2                /atan2(im(asin(x*y)), re(asin(x*y)))\     4 /   2                2                /atan2(im(asin(x*y)), re(asin(x*y)))\
\/  im (asin(x*y)) + re (asin(x*y)) *cos|-----------------------------------| + I*\/  im (asin(x*y)) + re (asin(x*y)) *sin|-----------------------------------|
                                        \                 2                 /                                             \                 2                 /
i(re⁡(asin⁡(xy)))2+(im⁡(asin⁡(xy)))24sin⁡(atan2⁡(im⁡(asin⁡(xy)),re⁡(asin⁡(xy)))2)+(re⁡(asin⁡(xy)))2+(im⁡(asin⁡(xy)))24cos⁡(atan2⁡(im⁡(asin⁡(xy)),re⁡(asin⁡(xy)))2)i \sqrt[4]{\left(\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)},\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)},\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)} \right)}}{2} \right)} 
=
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4 /   2                2                /atan2(im(asin(x*y)), re(asin(x*y)))\     4 /   2                2                /atan2(im(asin(x*y)), re(asin(x*y)))\
\/  im (asin(x*y)) + re (asin(x*y)) *cos|-----------------------------------| + I*\/  im (asin(x*y)) + re (asin(x*y)) *sin|-----------------------------------|
                                        \                 2                 /                                             \                 2                 /
i(re⁡(asin⁡(xy)))2+(im⁡(asin⁡(xy)))24sin⁡(atan2⁡(im⁡(asin⁡(xy)),re⁡(asin⁡(xy)))2)+(re⁡(asin⁡(xy)))2+(im⁡(asin⁡(xy)))24cos⁡(atan2⁡(im⁡(asin⁡(xy)),re⁡(asin⁡(xy)))2)i \sqrt[4]{\left(\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)},\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)},\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)} \right)}}{2} \right)} 
producto
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4 /   2                2                /atan2(im(asin(x*y)), re(asin(x*y)))\     4 /   2                2                /atan2(im(asin(x*y)), re(asin(x*y)))\
\/  im (asin(x*y)) + re (asin(x*y)) *cos|-----------------------------------| + I*\/  im (asin(x*y)) + re (asin(x*y)) *sin|-----------------------------------|
                                        \                 2                 /                                             \                 2                 /
i(re⁡(asin⁡(xy)))2+(im⁡(asin⁡(xy)))24sin⁡(atan2⁡(im⁡(asin⁡(xy)),re⁡(asin⁡(xy)))2)+(re⁡(asin⁡(xy)))2+(im⁡(asin⁡(xy)))24cos⁡(atan2⁡(im⁡(asin⁡(xy)),re⁡(asin⁡(xy)))2)i \sqrt[4]{\left(\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)},\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)},\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)} \right)}}{2} \right)} 
=
                                      I*atan2(im(asin(x*y)), re(asin(x*y)))
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4 /   2                2                                2                  
\/  im (asin(x*y)) + re (asin(x*y)) *e
(re⁡(asin⁡(xy)))2+(im⁡(asin⁡(xy)))24eiatan2⁡(im⁡(asin⁡(xy)),re⁡(asin⁡(xy)))2\sqrt[4]{\left(\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2}} e^{\frac{i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)},\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)} \right)}}{2}} 
(im(asin(x*y))^2 + re(asin(x*y))^2)^(1/4)*exp(i*atan2(im(asin(x*y)), re(asin(x*y)))/2)
Respuesta rápida [src] 
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     4 /   2                2                /atan2(im(asin(x*y)), re(asin(x*y)))\     4 /   2                2                /atan2(im(asin(x*y)), re(asin(x*y)))\
z1 = \/  im (asin(x*y)) + re (asin(x*y)) *cos|-----------------------------------| + I*\/  im (asin(x*y)) + re (asin(x*y)) *sin|-----------------------------------|
                                             \                 2                 /                                             \                 2                 /
z1=i(re⁡(asin⁡(xy)))2+(im⁡(asin⁡(xy)))24sin⁡(atan2⁡(im⁡(asin⁡(xy)),re⁡(asin⁡(xy)))2)+(re⁡(asin⁡(xy)))2+(im⁡(asin⁡(xy)))24cos⁡(atan2⁡(im⁡(asin⁡(xy)),re⁡(asin⁡(xy)))2)z_{1} = i \sqrt[4]{\left(\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)},\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\operatorname{asin}{\left(x y \right)}\right)},\operatorname{re}{\left(\operatorname{asin}{\left(x y \right)}\right)} \right)}}{2} \right)} 
z1 = i*(re(asin(x*y))^2 + im(asin(x*y))^2)^(1/4)*sin(atan2(im(asin(x*y), re(asin(x*y)))/2) + (re(asin(x*y))^2 + im(asin(x*y))^2)^(1/4)*cos(atan2(im(asin(x*y)), re(asin(x*y)))/2))
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