SOLUTION: How do you simplify ((1-2i)/(3+i)) and write in a+bi form?

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Question 6614: How do you simplify ((1-2i)/(3+i)) and write in a+bi form?
Answer by prince_abubu(198) (Show Source):
You can put this solution on YOUR website!
You believe that anything divided by itself = 1, right? And multiplying something by 1 doesn't change the original value?

We'll multiply both numerator and denominator with the denominator's conjugate. The conjugate is exactly the complex number a +/- bi EXCEPT that you flip the sign before the bi term. Since you've got 3 + i, the conjugate would be 3 - i. We'll multiply both numerator and denominator by the conjugate.

really is multiplying your original rational expression by 1, so it doesn't change anything. This is just a trick you can use.

Let's take care of the numerator first by performing FOIL:

Let's take the denominator and do FOIL

So, numerator over denominator would give you . They want it in a + bi form. Remember your fraction rule that says . So in this case, your answer will be