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In $46-60,$ write each quotient in $a+b i$ form.$$\frac{\frac{1}{7}+i}{\frac{5}{i}}$$

$\frac{1}{35} i-\frac{1}{5}$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 5

Operations with Complex Numbers

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

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01:32

In mathematics, the absolu…

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In $46-60,$ write each quo…

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R and this problem we were asked about the complex number 1/7 plus by the complex number five divided by. So the simplest way to simplify this is to acknowledge that we have a fraction and the denominator of the entire fraction. So to undo this fraction will need to multiple both the numerator and the denominator by ah, and that will cancel the in the denominator. So moving right along, we have I toms 17 plus I, which is gonna give us ah, divided by seven plus squared and the numerator and then five plus on Tom's I the eyes they're gonna cancel. It's just gonna leave us with a five. All right now, moving right along in the numerator we have won over seven I and then squared is the same thing as a negative one because it's the square root of negative one squared, which just leaves the negative one. So instead of squared, we have one son with a modest one and then in the denominator wish tohave five. Now we need our final answer to be in the form a plus B I for answer to be correct. So is the final step we have one. Oh, we need to be careful here because we actually have written the imaginary component first. Um, but technically speaking, the rial component, the A component is what needs to come first. So we have a modest one divided by five star riel. Component is modest. 1/5 and then our imaginary component is 1/7. Ah, divided by five. But this could be further simplified to give us a final answer of negative 1/5. All right. And then we're going to add one over 35 I and we do this by multiplying the top and the bottom of this fraction by seven. And it cancels this seven, and it makes this denominator 35. And our final answer, therefore, is negative. 1/5 plus one over 35.

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