SOLUTION: Give answer in a + bi form. 4 - 5i / 2 + 3i

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Question 124825: Give answer in a + bi form.
4 - 5i / 2 + 3i
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You need to remember the 'difference of two squares' factorization: %28a%2Bb%29%28a-b%29=a%5E2-b%5E2

What we want to accomplish is to get that pesky i out of our denominator. Using the difference of two squares idea, we see that we can accomplish this quite nicely by multiplying the denominator by 2-3i. Of course if we multiply the denominator by something, we must multiply the numerator by the same thing, so:

%28%284-5i%29%2F%282%2B3i%29%29%28%282-3i%29%2F%282-3i%29%29

Using the difference of two squares on the denominator, and FOIL on the numerator we obtain:

%288-12i-10i%2B15i%5E2%29%2F%284-9i%5E2%29.

Now, collect terms remembering that i%5E2=-1.

%28%28-7%29-22i%29%2F13

In a%2Bbi form you have: -%287%2F13%29-%2822%2F13%29i