Plotting Complex Variables on Argand Diagrams

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August 8th 2006, 06:38 AM
c00ky

Plotting Complex Variables on Argand Diagrams

Hello again guys,

I have the following problem:

Problem:

a) Plot the following complex variables on an Argand diagram

(i) 2 + j5
(ii) 3 - j6
(iii) - 4 + j10
(iv) - 6 - j3

b) Convert the (i) and (ii) above into their Polar Equivalents, show ALL working.

c) Add (i) and (ii) above and express the result in rectangular form.

d) Subtract (iii) from (ii) above and express the result in rectangular form.

e) Multiply (i) and (iii) above by first converting to Polar form and express the result in Polar form.

f) Divide (iii) by (iv) above by first converting to Polar form and express the result in Polar form.

IT'S PRETTY HARD I KNOW! can anbody help as i'm totally lost.
August 8th 2006, 07:31 AM
ThePerfectHacker

1 Attachment(s)

1)Look at diagram below.

2)Look at the first line. Let $\theta$ be the angle is forms. Then $\tan \theta = \frac{5}{2}=2.5$ . Thus, $\tan^{-1} (2.5)\approx 1.2$ .
The radius of this is, $\sqrt{2^2+5^2}=\sqrt{29}$ .
Therefore, expressed in polar form is,
$\sqrt{29}(\cos 1.2+i\sin 1.2)$

Look at the second line. Let $\psi$ be the angle it forms (acute). Then, $\tan \psi =\frac{6}{3}=2$ . Thus, $\psi = \tan^{-1}(2)\approx 1.1$ . The radius of this is, $\sqrt{3^2+6^2}=\sqrt{45}$ . Therefore, expressed in polar form is,
$\sqrt{45}[\cos (-1.1)+i\sin (-1.1)]$
Note the minus because we need it to give a minus in front of sine because the point is below x-axis.
August 8th 2006, 11:04 AM
c00ky

For the polar form of (ii) my answer is:

6.7 (the distance from 0,0)
and the angle as 63.43

Could somebody please verify these answers?

I perhaps think my angle is wrong, where must the points for the angle start and finish? I'm getting confused as to what happens when minus figures occur.

THANKS GUYS.