Question

The square roots of -18i are ______

Options

• 3 + 3i, -3 + 3i

• -3 - 3i, -3 + 3i

• 3 - 3i, 3 + 3i

• 3 - 3i, -3 + 3i

Answer 1

The square roots of -18i are 3 - 3i, -3 + 3i.

Explanation:

Let x + iy = `sqrt(-18i)`

⇒ x² - y² + 2xyi = -18i

∴ `x^2 - y^2 = 0` and 2xy = -18

Solving these equations, we get

x = 3, y = -3 and x = -3, y = 3

∴ Square roots are 3 - 3i, -3 + 3i.