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In $38-45,$ find the multiplicative inverse of each of the following in $a+b i$ form.$$3-3 i$$

$\frac{1+i}{6}$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 5

Operations with Complex Numbers

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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In $38-45,$ find the multi…

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Find the inverse of each r…

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In Exercises $35-42,$ find…

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Find the additive inverse …

the multiplication of inverse of three minus three. I would be 1/3, minus three I. But that's not the form were supposed to leave our answer in. We want to put it in standard form. And to get there, we need to multiply by a special form of one the congregate of the denominator three plus three I over itself that will help the denominators simplify. So our numerator is three plus three I and then the denominators We need to multiply together. So if we foil those, we got three plus 39 And then the outsides make plus nine I and the insides make minus nine I. So those councils cancel and then the last give us minus nine. I squared. Okay, remember that I squared is negative one. So we have three plus three I over nine, minus nine times negative one. That means we have three plus three I over nine plus 9 18 and noticed that we could factor three out of the numerator and reduce that with the 18 on the bottom. And I gives us 1/6. So we have one, plus I over six. Now, if we want to split that up into two separate parts, the rial part would be 1/6 and the imaginary part would be 1/6 I.

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