Question

How do you perform the operation and write the result in standard form given `(4+5i)^2`?

Answer 1

`(4+5i)^2=-9+40i`

Explanation:

Whenever multiplication or division operations of complex numbers one need to always remember that `i^2=-1`.

As such `(4+5i)^2`

= `4^2+2×4×5i+(5i)^2`

= `16+40i+25×(-1)`

= `16+40i-25`

= `-9+40i`