(-3i)^2

Jasonbradley

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Jun 16, 2024

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Simplifying (-3i)^2

In mathematics, the expression (-3i)^2 can be simplified using the rules of complex numbers.

Understanding Complex Numbers

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as √-1.

Simplifying (-3i)^2

1. Expand the expression: (-3i)^2 = (-3i) * (-3i)

2. Apply the distributive property: (-3i) * (-3i) = 9i^2

3. Substitute i^2 with -1: 9i^2 = 9(-1)

4. Simplify: 9(-1) = -9

Therefore, (-3i)^2 = -9.

Key Points

• The square of an imaginary number is always a real number.
• Remember that i^2 = -1.
• When simplifying complex numbers, follow the rules of arithmetic and algebra.