# State True or False for the following: The inequality |z – 4| < |z – 2| represents the region given by x > 3. - Mathematics

MCQ
True or False

State True or False for the following:

The inequality |z – 4| < |z – 2| represents the region given by x > 3.

• True

• False

#### Solution

This statement is True.

Explanation:

Given that: |z – 4| < |z – 2|

Let z = x + yi

⇒ |x + yi – 4| < |x + yi – 2|

⇒ |(x – 4) + yi| < |(x – 2) + yi|

⇒ sqrt((x - 4)^2 + y^2) < sqrt((x - 2)^2 + y^2)

⇒ (x – 4)2 + y2 < (x – 2)2 + y2

⇒ (x – 4)2 < (x – 2)2

⇒ x2 + 16 – 8x < x2 + 4 – 4x

⇒ –8x + 4x < –16 + 4

⇒ –4x < –12

⇒ x > 3

Concept: Algebraic Operations of Complex Numbers
Is there an error in this question or solution?

#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Exercise | Q 26.(vi) | Page 93

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