Chapter 7.2, Problem 21E

(a)

To determine

To prove: $x+yi$ satisfies the equation $z^2=a+bi$, where $x=\frac{b}{2y}$ and $y=\pm \sqrt{\frac{\sqrt{a^2+b^2}-a}{2}}$.

(b)

(i)

To determine

Two square roots of $3-4i$.

(ii)

To determine

Two square roots of $4+3i$.

(iii)

To determine

Two square roots of $5+12i$.

(iv)

To determine

Two square roots of $-12+5i$.