Multiply Write the answer in the form a+bi. (2-3i)^2
I am coming up with 4-3i what am I doing wrong?
To find the square of a complex number, you can use the FOIL method. "FOIL" stands for First, Outer, Inner, Last, and it helps you multiply two binomials.
Using the given expression, (2-3i)^2, we can rewrite it as (2-3i) × (2-3i).
Now let's apply the FOIL method:
First: Multiply the first terms of each binomial: (2 × 2) = 4.
Outer: Multiply the outer terms of each binomial: (2 × -3i) = -6i.
Inner: Multiply the inner terms of each binomial: (-3i × 2) = -6i.
Last: Multiply the last terms of each binomial: (-3i × -3i) = 9i^2.
Now we have:
4 + (-6i) + (-6i) + 9i^2.
Simplifying further:
4 + (-6i) + (-6i) + 9i^2 can be rewritten as 4 - 12i + 9i^2.
Since i^2 is defined as -1, we have:
4 - 12i + 9(-1).
Simplifying again:
4 - 12i - 9 = -5 - 12i.
So, the square of (2-3i) is -5 - 12i.