# If z is a complex number, then ______. - Mathematics

MCQ
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If z is a complex number, then ______.

• |z2| > |z|2

• |z2| = |z|2

• |z2| < |z|2

• |z2| ≥ |z|

#### Solution

If z is a complex number, then |z2| = |z|2.

Explanation:

Let z = x + yi

|z| = |z + yi| and |z|2 = |x + yi|2

⇒ |z|2 = x2 + y   ......(i)

Now z2 = x2 + y2i2 + 2xyi

z2 = x2 – y2 + 2xyi

|z|2 = sqrt((x^2 - y^2)^2 + (xy)^2)

= sqrt(x^4 + y^4 - 2x^2 y^2 + 4x^2 y^2)

= sqrt(x^4 + y^4 + 2x^2 y^2)

= sqrt((x^2 + y^2)^2

So |z2| = x2 + y2 = |z|2

So |z2| = |z|2

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 46 | Page 96

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