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STD 11 - 4.1 complex nubers — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.1 complex nubers4 Marks
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.$

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