Perform each operation. Write answers in standard form. (-12 -...

Question

Perform each operation. Write answers in standard form. (-12 -i) / (-2 -5i)

Accepted Answer

Hello everyone. We're going to divide the expression negative 60 plus 50 I Over negative 13 plus 21. I first thing I'm gonna do is rewrite this as a fraction. So negative 60 plus 50 I over negative 13 Plus 21. I Now looking at it I recall that I need to use a conjugate to get rid of the imaginary number in the denominator and that a conjugate is the same terms as my denominator but the opposite sign in the middle. So for this problem the conjugate is negative 13 -21. I and I'm gonna multiply numerator and denominator by this. So I'm gonna use foil to multiply out the top First gives me -60 times negative 13 to be a positive 780. Outer is negative 60 times negative 21 eye. So it's gonna be a positive I inner 50 I times negative 13 would give me a negative 650 I and last gives me let's see 50 I times negative 21 I So that's a negative 1050 I squared. I'm going to clean up my like terms and my eye squares and my next step Before I do that I wanna take care of the denominator. Conjugate are formed on purpose to be the difference of square. So I can square the first term. So 13 squared is 169 square. The last term. So 21 squared is 441 and the I squared part is I squared they put a minus in between them. So now I'm going to combine my like terms and I'm going to substitute negative one in four I squared So 780 stays the same. I'm gonna combine The positive i and the negative 650 I and I will get a positive 610 I and then minus 1050 and I'm going to substitute negative one in for I squared And do similar in the denominator 169 stays put 441 And then now time is -1. So right now I have 780 plus 610 I minus 1050 times negative one Over 169 -441 times negative one. I'm gonna multiply in those negative ones. So I have 780 plus 610. I -1050 times negative one will give me a positive 1050 In the denominator, 169 stays put -441, -1 is a positive 441. Right now I have a few more like terms I can combine. So in my numerator 780 plus 1050 would give me Plus 610. I in the denominator Adding 169 and Gives Me 610. So now I noticed that I have two numbers that are I think that's there on purpose. So we can reduce this. I'm gonna see if 600 tangos evenly into 8 1830 And it definitely does. It's definitely times three. So I'm going to factor 610 out of my numerator. So 610 Times in parentheses three plus I Over 610. And now I can reduce the 600 tens I'm left with three plus I. And that is my solution three plus I is in standard form because the real number part is first and that is answer choice a have a good day.

Perform each operation. Write answers in standard form. (-12 -i) / (-2 -5i)

Key Concepts

Complex Number Standard Form

Division of Complex Numbers

Complex Conjugate

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