Question

If w=3iz-z2 given that z=x+iy, find w2 in terms of xand y.

Select one:

A x4+y4+2x2y2-6x2y-6y3-9x2-9y2

B x4+y4+2x2y2-6x2y-6y3+9x2+9y2

C x4+y4+2x2y2-6x2y-6y3+9x2-9y2

D x4-y4+2x2y2-6x2y-6y3+9x2+9y2

Answer 1

$\left| w \right|^2=\left| z\left( z-3i \right) \right|^2=\left| z \right|^2\left| z-3i \right|^2=\\=\left( x^2+y^2 \right) \left( x^2+\left( y-3 \right) ^2 \right) =\\=x^4+x^2\left( y^2+\left( y-3 \right) ^2 \right) +y^2\left( y-3 \right) ^2=\\=x^4+y^4+2x^2y^2-6x^2y-6y^3+9x^2+9y^2\\B\,\,is\,\,correct$