Complex Numbers And Quadratic Equations question 442
Question: If $ z=1+i, $ then the multiplicative inverse of z2 is (where i = $ \sqrt{-1} $ ) [Karnataka CET 1999]
Options:
A) 2 si
B) 1 - i
C) - i/2
D) i/2
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ z=1+i $ and $ i=\sqrt{-1}. $ Squaring both sides, we get $ z^{2}={{(1+i)}^{2}}=1+2i+i^{2}=1+2i-1 $ or $ z^{2}=2i. $ Since it is multiplicative identity, therefore multiplicative inverse of $ z^{2}=\frac{1}{2i}\times \frac{i}{i}=\frac{i}{2i^{2}}=-\frac{i}{2}. $
BETA
