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JEE Main 2017 · Mathematics · Complex Numbers · medium

The value of ((1+i)^8/((1-i)^6 is

Single correct option

The value of (1+i)8(1−i)6\dfrac{(1+i)^8}{(1-i)^6} is
  1. A. 2i2i
  2. B. −2i-2i
  3. C. 22
  4. D. −2-2
Show answer and solution

Answer: (B) −2i-2i

Since (1+i)2=2i(1+i)^2=2i, we get (1+i)8=(2i)4=16(1+i)^8=(2i)^4=16. Similarly (1−i)2=−2i(1-i)^2=-2i, so (1−i)6=(−2i)3=−8i3=8i(1-i)^6=(-2i)^3=-8i^3=8i. Therefore the ratio is 168i=2i=−2i\dfrac{16}{8i}=\dfrac{2}{i}=-2i because 1/i=−i1/i=-i. Forgetting the sign of 1/i1/i leads to the distractor 2i2i.
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