( – 9+4i)2

Jasonbradley

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Jun 16, 2024

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Simplifying (-9 + 4i)²

This article will guide you through the process of simplifying the complex number expression (-9 + 4i)².

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 the square root of -1 (i² = -1).

Simplifying the Expression

To simplify (-9 + 4i)², we can use the FOIL method (First, Outer, Inner, Last) which is used for multiplying binomials.

1. Expand the expression: (-9 + 4i)² = (-9 + 4i)(-9 + 4i)

2. Apply the FOIL method:

   • First: -9 * -9 = 81
   • Outer: -9 * 4i = -36i
   • Inner: 4i * -9 = -36i
   • Last: 4i * 4i = 16i²

3. Combine the terms: 81 - 36i - 36i + 16i²

4. Substitute i² with -1: 81 - 36i - 36i + 16(-1)

5. Simplify: 81 - 36i - 36i - 16 = 65 - 72i

Final Answer

Therefore, the simplified form of (-9 + 4i)² is 65 - 72i.