Question

Complex number $z$ satisfying the equation $z^2\times (1+i)=-7+17i,$ is/are

• A. $z=-3+2i$
• B. $z=3+2i$
• C. $z=-3-2i$
• D. $z=3-2i$

Answer 1

Answer: (B), (C)

The correct options are
B $z=3+2i$
C $z=-3-2i$

$z^2\times (1+i)=-7+17i$

Let $z=x+iy,$ where $x,y\in R$
$\Rightarrow (x+iy{)}^2=\frac{-7+17i}{(1+i)}\Rightarrow x^2-y^2+2ixy=\frac{10+24i}{2}\Rightarrow x^2-y^2=5,2xy=12$

Solving the equations, we get
$x=3,y=2$ or $x=-3,y=-2$

Hence $z=3+2i$ or $z=-3-2i$