%5E2.jpeg "(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.