Convert each of the complex numbers given.
$$
-3
$$

Answer

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Algebra

NCERT Class 11 - Math

Chapter 5

Complex Numbers and Quadratic Equations

Section 2

Complex Numbers

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Video Transcript

Okay, so in this case, we're just given negative three I. So the first thing we want to do is convert that to a plus B. I form to be able to figure out where the coordinates gonna this is gonna be zero minus three I. So to graph this, I am going to go right and left. Zero. And I'm gonna go down three units and this is where the point would be where negative three I the point would be So now we just need to convert this into a polar form. So I remember the polar form is gonna be our co sign of my argument. Plus I sine of my argument. So let's find our modules or let's find our magnitude or module is first and that's really just the distance. Well, what's nice about this guy is we don't even have to use the Pythagorean theorem with a formal. We can actually just count. This is actually just three units, and now the only thing that we're missing is the argument. And again, this one, we don't have to even do any trick because you can see that it lies on the Y axis between the third and the fourth quadrant. In order to get between the third and the fourth quadrant, you would have to rotate 270 degrees, which would be your argument, and therefore this would be the polar form and the graph of the point negative three I.

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