Simplify each of the following and express it in the form (a + ib)

Given: $(-3+5 i)^{3}$

We know that,

$(-a+b)^{3}=-a^{3}+3 a^{2} b-3 a b^{2}+b^{3} \ldots$ (i)

So, on replacing a by 3 and b by 5i in eq. (i), we get

$-(3)^{3}+3(3)^{2}(5 i)-3(3)(5 i)^{2}+(5 i)^{3}$

$=-27+3(9)(5 i)-3(3)\left(25 i^{2}\right)+125 i^{3}$

$=-27+135 i-225 i^{2}+125 i^{3}$

$=-27+135 i-225 \times(-1)+125 i \times i^{2}$

$=-27+135 i+225-125 i\left[\because i^{2}=-1\right]$

$=198+10 i$