MCQ
The value of ${(1 + i)^8} + {(1 - i)^8}$ is
- A$16$
- B$-16$
- ✓$32$
- D$-32$
✓
Answer
Correct option: C.
$32$
c
(c) $\,{(1 + i)^2} = \,1 + {i^2} + 2i = 2i$and ${(1 - i)^2} = 1 + {i^2} - 2i = - 2i$
$ \Rightarrow {(1 + i)^8} + {(1 - i)^8} = {(2i)^4} + {( - 2i)^4}$$ = {2^4}({i^4} + {i^4})$
$ = {2^5} = 32.$
(c) $\,{(1 + i)^2} = \,1 + {i^2} + 2i = 2i$and ${(1 - i)^2} = 1 + {i^2} - 2i = - 2i$
$ \Rightarrow {(1 + i)^8} + {(1 - i)^8} = {(2i)^4} + {( - 2i)^4}$$ = {2^4}({i^4} + {i^4})$
$ = {2^5} = 32.$
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