Complex Numbers 1 Question 9

9.

The smallest positive integer n for which (1+i1−i)n=1, is

(a) 8

(b) 16

(c) 12

(d) None of these

(1980,2M)

Show Answer

Answer:

Correct Answer: 9. (d)

Solution:

  1. Since, (1+i1−i)n=1⇒(1+i1−i×1+i1+i)n=1

⇒2in2=1⇒in=1

The smallest positive integer n for which in=1 is 4 .

∴n=4

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