SOLUTION: Hey! So I came across a question that asks for the multiplicative inverse of 2+3i. I looked at the answer choices and determined that it's 1/2-3i. However, the key says that the an

Question 1150567: Hey! So I came across a question that asks for the multiplicative inverse of 2+3i. I looked at the answer choices and determined that it's 1/2-3i. However, the key says that the answer is 2-3i/13. Could I get an explanation as to why this is the answer? Thank you.
Found 4 solutions by josgarithmetic, MathTherapy, godlke321, ikleyn:
Answer by josgarithmetic(39614)   (Show Source): You can put this solution on YOUR website!
Did you try going this way and solve for the real and imaginary parts?

Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

Hey! So I came across a question that asks for the multiplicative inverse of 2+3i. I looked at the answer choices and determined that it's 1/2-3i. However, the key says that the answer is 2-3i/13. Could I get an explanation as to why this is the answer? Thank you.

I have absolutely no idea what the other person is referring to, by this: (a + bi)(2 + 3i). Anyway, the multiplicative inverse of 2 + 3i is its RECIPROCAL, or .
However, you'd then need to RATIONALIZE its denominator. If you don't know what I'm talking about, let me know and I'll explain the steps to get to the answer, which by the way, is CORRECT.
Answer by godlke321(1)   (Show Source): You can put this solution on YOUR website!
The answer to this problem is 1/2+3i
However, if the problem wants the answer in the simplest form (meaning that no i variable should be left on the denominator side. You will have to performs 1/2+3i times 2-3i/2-3i. This should lead you to get 2-3i/ 4-9i^2. i^2= -1
2-3i/4+9= 2-3i/13
Answer in simplest form: 2-3i/13
Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
.

Word-in-word this question was posted earlier to the forum and answered at

https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1150567.html

https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1150567.html

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