(4+6i)^2

2 min read Jun 16, 2024
(4+6i)^2

Squaring Complex Numbers: (4 + 6i)^2

This article will demonstrate how to square a complex number, specifically (4 + 6i)^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
  • i is the imaginary unit, defined as the square root of -1 (i.e., i² = -1)

Squaring (4 + 6i)

To square (4 + 6i), we need to multiply it by itself:

(4 + 6i)² = (4 + 6i) * (4 + 6i)

We can expand this using the FOIL (First, Outer, Inner, Last) method:

  • First: 4 * 4 = 16
  • Outer: 4 * 6i = 24i
  • Inner: 6i * 4 = 24i
  • Last: 6i * 6i = 36i²

Combining the terms:

16 + 24i + 24i + 36i²

Remember that i² = -1, so we can substitute:

16 + 24i + 24i + 36(-1)

Simplifying:

16 + 48i - 36

Finally, combining the real and imaginary terms:

-20 + 48i

Conclusion

Therefore, (4 + 6i)² equals -20 + 48i. This demonstrates how to square complex numbers by using the FOIL method and understanding the properties of the imaginary unit.

Related Post