Question

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

Answer 1

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`.