Complex Numbers And Quadratic Equations question 431
Question: If $ z=3-4i $ , then $ z^{4}-3z^{3}+3z^{2}+99z-95 $ is equal to
Options:
A) 5
B) 6
C) - 5
D) - 4
Show Answer
Answer:
Correct Answer: A
Solution:
Given that $ z=3-4i $
Þ $ z^{2}=-7-24i $ , $ z^{4}=-117-44i $ and $ z^{4}=-527+336i $ \ $ z^{4}-3z^{3}+3z^{2}+99z-95=5 $ Aliter: $ z=3-4i $
Þ $ {{(z-3)}^{2}}=-16 $
Þ $ z^{2}-6z+25=0 $ $ z^{4}-3z^{3}+3z^{2}+99z-95 $ $ =(z^{2}+3z-4)(z^{2}-6z+25)+5 $ $ =(z^{2}+3z-4)(0)+5=5 $
BETA
