Answer to Question #254156 in Complex Analysis for luzuko

Question

A complex number z satisfies the equation 

z^2\:=3+4i.

Which of the following is true about z?

1. (3+4i)^2=25+24i
2. z=+-(2+i)
3. (3+4i)^2=9+40i
4. z=+-(2+2i)
5. (3+4i)^2=7+24i

Answer 1

Taking into account that

$3+4i=4-1+4i=2^2+4i+i^2=(2+i)^2,$

we conclude that $z^2=(2+i)^2,$ and hence $z=\pm (2+i).$

Answer: 2