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Liberty University
Dividing Complex Numbers - Example 4


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plus I divided by one plus four I. In order to do that, we're going to multiply the fraction by the conduct of the denominator. So that's gonna be one minus four i for both of these. So we're gonna have to use full for both the numerator and the denominator. Remember, Full is multiplying the first terms outside terms, inside terms, last terms. So let's do our enumerators first. So that's three plus I times one minus four I so three times one would be three, three times negative. Four will be negative. 12 I one times I would be I and items negative. Four eyes negative. Four I square. So that's gonna give May I want We're gonna combine, like terms, but we're gonna leave her. I square there for now, so that would be three minus 12. I Excuse me, just say we're gonna combine like terms. So that's gonna be actually being negative. 11 I minus four. I squared over our denominator. We have one times one is one one times negative. Four eyes native, four I for items. One is for I. So those were gonna cancel out and four times negative. Four eyes Negative 16 I square. So I have one minus 16 I square. So let's simplify these. Some that we know that I squared is the same as negative one. So let's rewrite thes with that. So negative. So three minus 11 I minus four times negative. One over one, minus 16 times negative one that's gonna reduced to three minus 11. I plus four over one plus 16. So the whole thing reduces to seven minus 11 I over 15. So now that we have that, we can break this down into two separate fractions. So I have I'm sorry. That's gonna be 17. That's 15. So that's gonna be a 7/17, minus 11 over 17 I. So that's my solution.