(8+3i)^2 In Standard Form

Jasonbradley

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Jun 16, 2024

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Expanding (8 + 3i)² in Standard Form

In mathematics, 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, satisfying the equation i² = -1.

To express (8 + 3i)² in standard form, we will expand the expression using the FOIL method (First, Outer, Inner, Last) and simplify.

Expanding the Expression

1. (8 + 3i)² = (8 + 3i)(8 + 3i)
2. First: 8 * 8 = 64
3. Outer: 8 * 3i = 24i
4. Inner: 3i * 8 = 24i
5. Last: 3i * 3i = 9i²

Combining the terms, we get:

64 + 24i + 24i + 9i²

Simplifying the Expression

We know that i² = -1. Substituting this into our expression:

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

Simplifying further:

64 + 24i + 24i - 9

Combining like terms:

55 + 48i

Final Answer

Therefore, (8 + 3i)² expressed in standard form is 55 + 48i.