MHT CET · Maths · Complex Number
The value of \((1+i)^5(1-i)^7\)
- A -64
- B -64 i
- C 64 i
- D 64
Answer & Solution
Correct Answer
(B) -64 i
Step-by-step Solution
Detailed explanation
\( (1+i)^5(1-i)^7 \)
\( = (1+i)^5(1-i)^5(1-i)^2=[(1+i)(1+i)(1-i)]^5\) \(\left(1-2 i+i^2\right) \)
\( = \left(1-i^2\right)^5(-2 i)=(2)^5(-2 i)=-64 i \ldots\left[\because i^2=-1\right]\)
\( = (1+i)^5(1-i)^5(1-i)^2=[(1+i)(1+i)(1-i)]^5\) \(\left(1-2 i+i^2\right) \)
\( = \left(1-i^2\right)^5(-2 i)=(2)^5(-2 i)=-64 i \ldots\left[\because i^2=-1\right]\)
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