# If (1+i1-i)x = 1, then ______. - Mathematics

MCQ
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If ((1 + i)/(1 - i))^x = 1, then ______.

#### Options

• x = 2n + 1

• x = 4n

• x = 2n

• x = 4n + 1, where n ∈ N

#### Solution

If ((1 + i)/(1 - i))^x = 1, then x = 4n.

Explanation:

Given that: ((1 + i)/(1 - i))^x = 1

⇒ (((1 + i)(1 + i))/((1 - i)(1 - i)))^x = 1

⇒ ((1 + i^2 + 2i)/(1 - i^2))^x = 1

⇒ ((1 - 1 + 2i)/(1 + 1))^x = 1

⇒ ((2i)/2)^x = 1

⇒ (i)x = (i)4n

⇒ x = 4n, n ∈ N

Concept: Algebraic Operations of Complex Numbers
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Exercise | Q 39 | Page 95

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