Complex Numbers And Quadratic Equations question 401
Question: The value of $ {{(1+i)}^{8}}+{{(1-i)}^{8}} $ is [RPET 2001; KCET 2001]
Options:
A) 16
B) - 16
C) 32
D) - 32
Show Answer
Answer:
Correct Answer: C
Solution:
$ \because {{(1+i)}^{2}}=1+i^{2}+2i=2i $ and $ {{(1-i)}^{2}}=1+i^{2}-2i=-2i $
$ \Rightarrow {{(1+i)}^{8}}+{{(1-i)}^{8}}={{(2i)}^{4}}+{{(-2i)}^{4}} $ $ =2^{4}(i^{4}+i^{4}) $ $ =2^{5}=32. $
BETA
