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.

−4i

Accepted Answer

But the given complex number on the graph express the complex number in the polar form. But we have negative to I, if you notice here, we have the complex plane that was first plot the number on the graph, we have negative two I no. The form of a complex number is Z equals X plus Y I where X will be the direction we move on the real axis. Y will be the direction we move on the complex axis. Now we notice we do not have an X in our function. We will say that's a zero minus two I four ry I, this means we will move on our imaginary axis down by two. And because we're not shifting on the real axis, our point occurs at zero negative two. Now let's write the number in polar form. We can express hours in polar form by using formula Z equals R cosine data plus I sine data where R is the square root of X squared plus Y squared. And data will be the art tangent or the inverse tangent stands to net the first of Y divided by X. Now let's find the R first R will be the square root A zero squared plus negative two square. This gives us the square of four, which is just two. Now we have data equals the inverse tangent negative two divided by zero. Now this is a little weird because we have a division by zero. But if we were to find this angle on our unit circle, this angle will occur at three pi divided by two. We can now write our equation to see equals are R two. So three pi divided by two because I sine three pi divided by two because this is our equation of our number. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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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. −4i