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MCQ

Fill in the Blanks

The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.

#### Options

|z|

^{2}`|barz|^2`

`|z|^2/2`

None of these

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#### Solution

The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is **`underlinebb(|z|^2/2)`**.

**Explanation:**

Let z = x + iy.

Then –iz = y – ix.

Therefore, z + iz = (x – y) + i(x + y)

Required area of the triangle = `1/2(x^2 + y^2) = |z|^2/2`.

Concept: Algebraic Operations of Complex Numbers

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