Question

How do you multiply `(3+5i)^2`?

Answer 1

The answer is `-16+30i`

Explanation:

To square a complex number you do a similar action as if you were to square an expression like `(a+bx)`. The only difference is you have to remember that `i^2=-1`

So:

`(3+5i)^2=3^2+2*3*5i+(5i)^2=9+30i+25i^2`
`=9+30icolor(red)(-25)=9-25+30i=-16+30i`

The minus sign in the marked expression comes from the fact that `i^2=-1`