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MCQ

True or False

**State True or False for the following:**

If z is a complex number such that z ≠ 0 and Re(z) = 0, then Im(z^{2}) = 0.

#### Options

True

False

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#### Solution

This statement is **False**.

**Explanation:**

Let z = x + yi, z ≠ 0 and Re(z) = 0

Since real part is 0.

⇒ x = 0

∴ z = 0 + yi = yi

∴ lm(z^{2}) = y^{2}i^{2}

= –y^{2} which is real.

Concept: The Modulus and the Conjugate of a Complex Number

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