# Tutor.com Complex Numbers Session

##### Apr. 11, 2012

Session Transcript - Math - Trigonometry, 4/4/2012 1:44PM - Tutor.comSession Date: 4/4/2012 1:44PM
Length: 19.4 minute(s)
Subject: Math - Trigonometry

System Message
[00:00:00] *** Please note: All sessions are recorded for quality control. ***

jared (Customer)
[00:00:00] plot each complex number. Then write the complex number in polar form.

James S (Tutor)
[00:00:15] Hello, welcome to Tutor.com !

jared (Customer)
[00:00:25] hello

James S (Tutor)
[00:00:44] Have you done problems like this before?

jared (Customer)
[00:00:49] no

James S (Tutor)

jared (Customer)
[00:01:51] ok

James S (Tutor)
[00:02:22] it's actually very similar to plotting regular coordinates.

jared (Customer)
[00:02:30] ok

James S (Tutor)
[00:02:41] the real number part is along the x axis, and the imaginary part is along the y axis

jared (Customer)
[00:02:58] so 3.464 =x and -2i =y?

James S (Tutor)
[00:03:29] That's right, though when we graph it we don't pay attention to the i, just the -2

jared (Customer)
[00:03:35] ok

James S (Tutor)
[00:04:31] So our point would be right there. Does that make sense?

jared (Customer)
[00:04:41] yes

James S (Tutor)
[00:05:00] Great! now for polar form. Have you been over that in class?

jared (Customer)
[00:05:15] yes

James S (Tutor)
[00:05:25] Great!
[00:06:15] Do you remember how to calculate r?

jared (Customer)
[00:07:02] --->

James S (Tutor)
[00:07:08] perfect!
[00:07:35] we can use 2sqrt 3 for a and -2 for b

jared (Customer)
[00:08:42] ok

James S (Tutor)
[00:08:48] What would that give us for r?

jared (Customer)
[00:09:05] r=4?

James S (Tutor)
[00:09:11] you got it!
[00:09:30] Now for the angle..do you remember how to find that?

jared (Customer)
[00:09:58] no

James S (Tutor)
[00:10:25] ok, for that we'll use tan -1

jared (Customer)
[00:10:50] so tan theta = inverse tan (y/x)?

James S (Tutor)
[00:11:29] close! no need for the tan on the left side, it's just theta = inverse tan (y/x)
[00:11:39] But there is one little trick to using this

jared (Customer)
[00:11:38] ok

James S (Tutor)
[00:12:42] There are two possible angles where the tangent is 1/sqrt3
[00:12:59] sorry, -1/sqrt3
[00:13:21] that happens at both 150 degrees and at 330 degrees

jared (Customer)
[00:14:01] how would it be 150 as well?

James S (Tutor)
[00:14:38] remember, tangent is negative in both the second and fourth quadrants

jared (Customer)
[00:14:54] correct

James S (Tutor)
[00:15:21] So there is would be another angle in the second quadrant where tan = -1/sqrt3

jared (Customer)
[00:15:37] alright

James S (Tutor)
[00:15:46] and it's 180 degrees from the other angle

jared (Customer)
[00:16:00] ok

James S (Tutor)
[00:16:11] So, to know which angle we need, we look at the graphs

jared (Customer)
[00:16:15] ok

James S (Tutor)
[00:16:26] when we did our graph, the point was in the fourth quadrant, right?

jared (Customer)
[00:16:44] yes

James S (Tutor)
[00:17:03] since the point is in the fourth quadrant, our angle will be too..so we'll need to use 330

jared (Customer)
[00:17:12] ok

James S (Tutor)
[00:17:34] and there is our polar form
[00:17:38] does that all make sense?

jared (Customer)
[00:18:09] you mean---->

James S (Tutor)
[00:18:39] I'm sorry, yes you are correct, thank you

jared (Customer)
[00:18:49] ok

James S (Tutor)
[00:18:57] good catch