In Exercises 11–26, plot each complex number. Then write the comp...

Question

In Exercises 11–26, plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians.

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Accepted Answer

Welcome back everyone. In this problem, we want to plot the number seven negative seven on a graph and then express that complex number in the polar form. Now, what do we know? Well, here our number is just a real number. So there is no imaginary part. So in other words, we could say that negative seven actually equals negative seven plus zero I since it has no imaginary part. So if we were to plot this on our graph, that represents where the real axis represents real numbers and the imaginary axis represents imaginary numbers, then our coordinate would have been negative 70. And when we plot that on our graph, it would be right at that point. So that would be our plot. Now, if we were to express it in polar farm, the problem is is that right now it's in rectangular farm. So we will need to convert it to polar form. No, recall that for a complex number written in rectangular form. Yeah, then in polar form, that complex number would have been R multiplied by the cosine of theta plus I multiplied by sine theta. OK. Where are equals the square root of the sum of X squared plus Y squared and theater equals the arc tangent of Y divided by X. Now, the good thing is I already know what my values of X and Y are because X is negative seven and Y is zero. So I can substitute those to get values for R and then write my number in pull R form. So let's do that. Let's first start with R. So R would be equal to the square root of negative seven squared plus zero squared, no negative seven squared, that's 49 and zero squared is zero. So I just have the square root of 49 which which equals seven. So R would be equal to seven. Next theater would be equal to the arc tangent of Y which is zero divided by 70, divided by seven is zero and no, the a tangent of zero equals pi because essentially what we are asking ourselves what anger, the tangent of what anger gives us zero. And that would have been pi so since theta is pi and are equals seven, then in polar form, that means our complex number could be written as seven multiplied by the cosine of theta plus I multiplied by the sign of theta. Thanks for watching everyone. I hope this video helped.

In Exercises 11–26, plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. −3

Key Concepts

Complex Numbers

Polar Form of Complex Numbers

Magnitude and Argument

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