Complex Numbers And Quadratic Equations question 52
Question: If $ z=3+5i,\text{then }z^{3}+\bar{z}+198= $ [EAMCET 2002]
Options:
A) $ -3-5i $
B) $ -3+5i $
C) $ 3+5i $
D) $ 3-5i $
Show Answer
Answer:
Correct Answer: B
Solution:
$ z=3+5i $ , $ \bar{z}=3-5i $
$ \Rightarrow $ $ z^{3}={{(3+5i)}^{3}}=3^{3}+{{(5i)}^{3}}+3.3.5i(3+5i) $ $ =-198+10i $ Hence, $ z^{3}+\bar{z}+198=10i-198+3-5i+198=3+5i $ .
BETA
