If z = 3 - 4 i , then the value of expression z4 - 3 z3 + 3 z2 + 99 z - 95 is equal to

Question

If z = 3 - 4 i , then the value of expression z4 - 3 z3 + 3 z2 + 99 z - 95 is equal to (A) 5 (B) 6 (C) - 5 (D) - 4

Tardigrade Admin · Accepted Answer

z = 3 - 4 i ⇒ (. z - 3 .)2 = - 16 ⇒ z2 - 6 z + 25 = 0 ⇒ z4-3z3+3z2+99z-95 = (. z2 + 3 z - 4 .) (. z2 - 6 z + 25 .) + 5 = (. z2 + 3 z - 4 .) (. 0 .) + 5 = 5

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

$5$

$6$

$- 5$

$- 4$

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

Q. If z=3−4i , then the value of expression z4−3z3+3z2+99z−95 is equal to

5

6

−5

−4

z=3−4i ⇒ (z−3)2=−16 ⇒ z2−6z+25=0 ⇒z4−3z3+3z2+99z−95 =(z2+3z−4)(z2−6z+25)+5 =(z2+3z−4)(0)+5=5

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

$5$

$6$

$- 5$

$- 4$

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