Question

If $z = 3 - 4 i$ , then the value of expression $z^{4} - 3 z^{3} + 3 z^{2} + 99 z - 95$ is equal to

• A. $5$
• B. $6$
• C. $- 5$
• D. $- 4$

Answer 1

Answer: (A)

$z = 3 - 4 i$ $\Rightarrow $ $\left(\right. z - 3 \left.\right)^{2} = - 16$
$\Rightarrow $ $z^{2} - 6 z + 25 = 0$
$\Rightarrow z^{4}-3z^{3}+3z^{2}+99z-95$ $= \left(\right. z^{2} + 3 z - 4 \left.\right) \left(\right. z^{2} - 6 z + 25 \left.\right) + 5$ $= \left(\right. z^{2} + 3 z - 4 \left.\right) \left(\right. 0 \left.\right) + 5 = 5$