Question

what is the square root of 3+4i? explain please.

Answer 1

\[
\sqrt{3+4 i}=(a+i b)\\
3+ 4 i = a^2 - b^2 + 2 a b i
a^2 - b^2 =3\\
2 a b = 4
\]
Solve for a and b

Answer 2

One of the solution is a=2 and b=1

Answer 3

2 + i is the answer

Answer 4

yes it has two answers

Answer 5

Of course -(2 + i) is a solution

Answer 6

z^1/n has n different solutions .always!

Answer 7

Unless z =0.

Answer 8

yeap