%5E2.jpeg "(8-3i)^2")
Squaring Complex Numbers: A Step-by-Step Guide for (8-3i)^2
This article will guide you through the process of squaring the complex number (8-3i).
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.
Squaring (8-3i)
To square (8-3i), we simply multiply it by itself:
(8-3i)^2 = (8-3i) * (8-3i)
To perform this multiplication, we can use the FOIL method:
- First: 8 * 8 = 64
- Outer: 8 * -3i = -24i
- Inner: -3i * 8 = -24i
- Last: -3i * -3i = 9i^2
Remember that i^2 = -1, so we can simplify the last term:
9i^2 = 9(-1) = -9
Now, we combine the terms:
64 - 24i - 24i - 9 = 55 - 48i
Conclusion
Therefore, (8-3i)^2 is equal to 55 - 48i. By following the steps outlined above, you can confidently square any complex number.