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

Given, 1−i(1+i)n=1⇒(1−i)(1+i(1+i)(1+i)n=1⇒22in=1in=1The smallest integral value of n will be 4.

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The smallest positive integer n for which {(1 + i)}{ (1-i)}^n

Question

The smallest positive integer $n$ for which $\frac{( 1 + i )}{( 1 - i )}^{n} = 1$ is

n = 8

n = 16

n = 12

none of these

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Lucas Discussed

The smallest positive integer

n

for which

\frac{( 1 + i )}{( 1 - i )}^{n} = 1

8 mins ago

Discuss this question LIVE

8 mins ago

Given,

\frac{( 1 + i )}{1 - i}^{n} = 1

\Rightarrow \frac{( 1 + i ) ( 1 + i )}{( 1 - i ) ( 1 + i}^{n} = 1

\Rightarrow \frac{2 i}{2}^{n} = 1

i^{n} = 1

The smallest integral value of

n

will be

4

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Question Text	The smallest positive integer $n$ for which $\frac{( 1 + i )}{( 1 - i )}^{n} = 1$ is
Answer Type	Text solution:1
Upvotes	150