Question

If $z=3+2i$, then value of $3z^3-13z^2+9z+65$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

Given : $3z^3-13z^2+9z+65$
Now,
$z=3+2i\Rightarrow (z-3{)}^2=4i^2\Rightarrow z^2-6z+13=0\cdots (1)$

Using equation $\left(1\right)$, we get
$3z^3-13z^2+9z+65=3z(z^2-6z+13)+5z^2-30z+65=0+5(z^2-6z+13)=0$