(9+4i)^2

Jasonbradley

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Jun 16, 2024

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Squaring Complex Numbers: (9 + 4i)²

This article explores the process of squaring the complex number (9 + 4i).

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).

Squaring (9 + 4i)

To square (9 + 4i), we simply multiply it by itself:

(9 + 4i)² = (9 + 4i)(9 + 4i)

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

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

Combining these terms, we get:

81 + 36i + 36i + 16i²

Since i² = -1, we can substitute:

81 + 36i + 36i + 16(-1)

Simplifying:

81 + 36i + 36i - 16

Combining real and imaginary terms:

65 + 72i

Conclusion

Therefore, (9 + 4i)² equals 65 + 72i.