(3-6i)^2

2 min read Jun 16, 2024
(3-6i)^2

Squaring Complex Numbers: (3-6i)^2

This article explores the squaring of the complex number (3 - 6i). We'll use the fundamental properties of complex numbers to find the solution.

Understanding Complex Numbers

Complex numbers are numbers of the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, defined as the square root of -1 (i² = -1).

Squaring (3 - 6i)

To square (3 - 6i), we multiply it by itself:

(3 - 6i)² = (3 - 6i) * (3 - 6i)

We can expand this using the distributive property (FOIL method):

(3 - 6i) * (3 - 6i) = 3 * 3 + 3 * (-6i) - 6i * 3 - 6i * (-6i)

Simplifying the terms:

= 9 - 18i - 18i + 36i²

Since i² = -1, we can substitute:

= 9 - 18i - 18i + 36(-1)

Combining the real and imaginary terms:

= 9 - 36 - 18i - 18i

= -27 - 36i

The Solution

Therefore, (3 - 6i)² = -27 - 36i.

This demonstrates that squaring a complex number results in another complex number, with both real and imaginary components.

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