# The complex number z which satisfies the condition |i+zi-z| = 1 lies on ______. - Mathematics

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The complex number z which satisfies the condition |(i + z)/(i - z)| = 1 lies on ______.

#### Options

• Circle x2 + y2 = 1

• The x-axis

• The y-axis

• The line x + y = 1.

#### Solution

The complex number z which satisfies the condition |(i + z)/(i - z)| = 1 lies on the x-axis.

Explanation:

Given that: |(i + z)/(i - z)| = 1

Let z = x + yi

∴ |(i + x + yi)/(i - x - yi)| = 1

⇒ |(x + (y + 1)i)/(-x - (y - 1)i)| = 1

⇒ |x + (y + 1)i| = |-x - (y - 1)i|

⇒ sqrt(x^2 + (y + 1)^2) = sqrt(x^2 + (y - 1)^2)

⇒ x2 + (y + 1)2 = x2 + (y – 1)2

⇒ (y + 1)2 = (y – 1)2

⇒ y2 + 2y + 1 = y2 – 2y + 1

⇒ 2y = –2y

⇒ 4y = 0

⇒ x-axis.

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 45 | Page 96

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