In Exercises 1–10, plot each complex number and find its absolute...

Question

In Exercises 1–10, plot each complex number and find its absolute value.

z = 4i

Accepted Answer

Welcome back. I am so glad you're here. We are asked to plot the given complex number on a graph and determine its absolute value. Our given complex number is Z equals nine. I. Then we're given a graph, it is on the complex plane. So we have a vertical imaginary axis and a horizontal real axis. They come together the origin in the middle. The domain for what's shown for our real axis is from negative 10 to positive 10. And the range for what's shown for our imaginary axis is from negative 10 to positive 10 as well. All right. So we're talking about complex numbers, complex numbers are typically given to us in the form of Z equals A plus B I. And we know a little bit of information about these values A is going to be our horizontal component that's going to be along our real access B is going to be our vertical component that's going to be a long hour imaginary axis. And that one's easier to remember because it's attached to that I that imaginary number. So we've got our A and our B which tell us where to plot this looking at our Z equals nine I, we can identify the one that's being multiplied by the I, our B component. That's going to be a positive nine. But where's our A value? Well, we could also write this as Z equals zero plus nine I, there are zero A s here. So our A value, our horizontal component is zero. Now to plot this from the origin. For our A value, we're going neither left nor right because that's zero. And for our B value, we're going to go up nine positive units from the origin. And here is our complex number. It's at zero nine on the complex plane. So we've plotted this great. Now, let's figure out the absolute value will we recall from previous lessons that the absolute value of a real number is the distance from zero on a number line. The absolute value of a complex number is the distance from the origin to Z. And the way we find this is we take, the absolute value of Z is equal to the square rut of A squared plus B squared. Well, we know our A and our B so we're just plugging those in and simplifying A is zero. So we have zero squared plus B is +99 squared, zero, squared is zero plus nine squared, nine squared is 81. So zero plus 81 is 81. We have the square root of 81 which is nine. So our absolute value of our complex number is nine and there's our graph and there's our absolute value. Well done. We'll catch you on the next one.

In Exercises 1–10, plot each complex number and find its absolute value. z = 4i

Key Concepts

Complex Numbers

Plotting Complex Numbers

Absolute Value of Complex Numbers

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