Question

Present the following complex number in polar form: z = 1/2 – j?3/2. Select one: a. z = cos(?/3) – j·sin(?/3)] b. z = 2[cos(?/6) – j·sin(?/6)] c. z = cos(5?/6) + j·sin(5?/6) d. z = 3[cos(?/6) + j·sin(?/6)] e. z = 3[cos(5?/3) + j·sin(5?/3)]

          Present the following complex number in polar form: z = 1/2 – j?3/2.

Select one:

a.
z = cos(?/3) – j·sin(?/3)]


b.
z = 2[cos(?/6) – j·sin(?/6)]


c.
z = cos(5?/6) + j·sin(5?/6)


d.
z = 3[cos(?/6) + j·sin(?/6)]


e.
z = 3[cos(5?/3) + j·sin(5?/3)]

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Precalculus Mathematics for Calculus

James Stewart, Lothar Redlin, Saleem… 7th Edition

Chapter 8

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Solved by Expert Karan Soni

03/15/2022

Step 1

Step 1:** Given complex number: \( z = \frac{1}{2} - j\frac{3}{2} \) ** Show more…

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Present the following complex number in polar form: z = 1/2 – j?3/2. Select one: a. z = cos(?/3) – j·sin(?/3)] b. z = 2[cos(?/6) – j·sin(?/6)] c. z = cos(5?/6) + j·sin(5?/6) d. z = 3[cos(?/6) + j·sin(?/6)] e. z = 3[cos(5?/3) + j·sin(5?/3)]

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Transcript

0:00 Hello everyone.

00:01 In this question we are given with a complex number and we have to express this particular complex number in polar form.

00:07 So here the complex number is given as z equals to half minus j times of root 3 by 2.

00:14 This is the given complex number.

00:17 Now what we will do is we will first express it in the plane.

00:23 Let's say this is for real part and this axis is for imaginary part.

00:33 Now we know that a complex number can be expressed as r cost theta plus j r sine theta.

00:42 And this particular format of complex number is known as polar form.

00:47 It's known as polar form.

00:50 So for expressing in the polar form we have to find out the value of r and theta.

00:54 We need two things, r and theta for expressing the complex number in the folder form.

01:01 Okay.

01:01 Now as you can clearly see on real axis.

01:03 We have half units.

01:05 So let's say this is half units and on imaginary axis we have minus root 3 by 2 units.

01:10 So let's say this is again negative side of minus root 3 by 2.

01:15 Now let us assume that they intersect at a point.

01:18 Okay...

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