%5E2.jpeg "(6-2i)^2")
Simplifying (6-2i)^2
In this article, we'll explore how to simplify the expression (6-2i)^2.
Understanding Complex Numbers
Before we start, let's quickly review 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.
Expanding the Expression
To simplify (6-2i)^2, we can use the FOIL method (First, Outer, Inner, Last) for expanding binomials.
Step 1: Expand the expression using FOIL: (6 - 2i) * (6 - 2i) = (6 * 6) + (6 * -2i) + (-2i * 6) + (-2i * -2i)
Step 2: Simplify: = 36 - 12i - 12i + 4i^2
Step 3: Substitute i^2 with -1: = 36 - 12i - 12i + 4(-1)
Step 4: Combine real and imaginary terms: = 36 - 4 - 12i - 12i
Step 5: Simplify: = 32 - 24i
Final Answer
Therefore, (6 - 2i)^2 simplifies to 32 - 24i.