(8+3i)2

2 min read Jun 16, 2024
(8+3i)2

Expanding (8 + 3i)<sup>2</sup>

This article will walk through the process of expanding and simplifying the expression (8 + 3i)<sup>2</sup>, where 'i' represents the imaginary unit (√-1).

Understanding the Basics

  • Imaginary Unit: The imaginary unit 'i' is defined as the square root of -1. This allows us to work with the square roots of negative numbers.
  • Complex Numbers: A complex number is a number of the form a + bi, where a and b are real numbers and 'i' is the imaginary unit.

Expanding the Expression

To expand (8 + 3i)<sup>2</sup>, we use the FOIL method:

  1. First: 8 * 8 = 64
  2. Outer: 8 * 3i = 24i
  3. Inner: 3i * 8 = 24i
  4. Last: 3i * 3i = 9i<sup>2</sup>

Combining the terms: 64 + 24i + 24i + 9i<sup>2</sup>

Simplifying the Expression

Remember that i<sup>2</sup> = -1. Substituting this into our expression:

64 + 24i + 24i + 9(-1)

Simplifying further:

64 + 48i - 9

Final Result

Combining real and imaginary terms:

(8 + 3i)<sup>2</sup> = 55 + 48i

Therefore, the simplified form of (8 + 3i)<sup>2</sup> is 55 + 48i.

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