%5E2.jpeg "(8-2i)^2")
Expanding (8-2i)^2
This article will explore the expansion of the complex number (8-2i)^2.
Understanding Complex Numbers
Complex numbers are numbers of the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, defined as ā-1.
Expanding the Expression
To expand (8-2i)^2, we can use the FOIL method (First, Outer, Inner, Last):
(8-2i)^2 = (8-2i) * (8-2i)
- First: 8 * 8 = 64
- Outer: 8 * -2i = -16i
- Inner: -2i * 8 = -16i
- Last: -2i * -2i = 4i^2
Now we combine the terms and remember that i^2 = -1:
64 - 16i - 16i + 4(-1) = 64 - 32i - 4
Finally, we simplify the expression:
(8-2i)^2 = 60 - 32i
Conclusion
Therefore, the expansion of (8-2i)^2 results in the complex number 60 - 32i. This process demonstrates how to expand complex numbers by using the FOIL method and applying the fundamental property of the imaginary unit, i^2 = -1.