If $\text{x}=\text{3}+\text{4i}$ ( where , $i=\sqrt{-1}$) the value of  $x^4-12x^3+70x^2-204x+225$ is

Hint  ${(x-3)}^2={\left(4i\right)}^2\Rightarrow x^2-6x=-25$

The given expression is $x^4-12x^3+70x^2-204x+225$

$$\begin{gathered} x^2\left(x^2-6x\right)-6x\left(x^2-6x\right)+34\left(x^2-6x\right)+225 \\ =x^2\left(-25\right)-6x\left(-25\right)+34\left(-25\right)+9\left(25\right) \\ =-25\left(x^2-6x+25\right) \\ =-25\left(-25+25\right) \\ =-25\left(0\right) \\ =0 \end{gathered}$$