Test 4 Section 3 #14

When you’re dividing complex numbers, you have to multiply the top and bottom of the fraction by the complex conjugate of the bottom. This creates a real number in the bottom of the fraction, which is awesome.

The bottom of this fraction is 3-2i, so its complex conjugate is 3+2i. To get started, then, we write the following:


Then we simplify as much as we can. First we FOIL:


Now, remembering that i=\sqrt{-1} and therfore that i^2=-1, we make that substitution and simplify further:


So there you have it. Once we simplify that complex fraction into a+bi form, we see that it’s just 2+i, which means a=2.

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