# Argand diagram

• Sep 15th 2010, 08:10 PM
brumby_3
Argand diagram
Draw each of the following complex numbers on an Argand diagram, and find their modulus and argument.

a) (1/2, -1/sqrt12)
b) -2i
c) -sqrt3 + sqrt(3i)

I think I know how to draw the complex numbers on the diagram, but what does it mean by modulus and argument? Can someone explain the steps to me please?
• Sep 15th 2010, 08:35 PM
mr fantastic
Quote:

Originally Posted by brumby_3
Draw each of the following complex numbers on an Argand diagram, and find their modulus and argument.

a) (1/2, -1/sqrt12)
b) -2i
c) -sqrt3 + sqrt(3i)

I think I know how to draw the complex numbers on the diagram, but what does it mean by modulus and argument? Can someone explain the steps to me please?

Have you been taught the polar form of a complex number?
• Sep 15th 2010, 09:07 PM
brumby_3
Quote:

Originally Posted by mr fantastic
Have you been taught the polar form of a complex number?

Hmm... do you mean a+bi? Like for example with a) (1/2, -1/sqrt12) I get 1/2 + (-1/sqrt12i) And then do I just plot this onto the Argand diagram (I know how to do that)? Am I on the right track? But I'm not sure what it's saying by modulus and argument?
• Sep 15th 2010, 09:08 PM
mr fantastic
Quote:

Originally Posted by brumby_3
Hmm... do you mean a+bi? Like for example with a) (1/2, -1/sqrt12) I get 1/2 + (-1/sqrt12i) And then do I just plot this onto the Argand diagram (I know how to do that)? Am I on the right track? But I'm not sure what it's saying by modulus and argument?

4. Polar Form of Complex Numbers
• Sep 15th 2010, 09:25 PM
brumby_3
I still don't know how to do the first question. :S
• Sep 16th 2010, 03:36 AM
HallsofIvy
Doesn't your text book, if it has problems asking for "modulus" and "argument", have definitions of those terms?

Writing a complex number in the form "x+ iy" is "Cartesian form" since it is using the x and y values of a Cartesian coordinate system on the Argand plane. "Polar form" is of the form " $r(cos(\theta)+ i sin(\theta))$" or (more advanced) " $re^{i\theta}$" where r is the straight line distance from (0,0) (the number 0) to (x, y) (the number x+iy) and $\theta$ is that angle the line from the origin to the number makes with the number- in other worlds "polar coordinates".

In any case, the "modulus" of a complex number, also called its "absolute value", is the distance, r, and the "argument" is the angle $\theta$. If, from the point (x, y) (representing x+ iy), you drew the line from (0, 0) to (x, y), the line from (x,y) to (x, 0), and the line from (0, 0) to (x, 0), you get a right triangle with sides of length x, y, and r, and angle at the origin $\theta$. From the Pythagorean theorem, $r^2= x^2+ y^2$ so that $r= \sqrt{x^2+ y^2}$. From the definition of the "tangent" function, $tan(\theta)= \frac{y}{x}$ so that $\theta= tan^{-1}\left(\frac{y}{x}\right)$ (as long as x is not 0 in which case the argument is infinite). I'll bet your text book has those formulas.
• Sep 16th 2010, 04:28 AM
mr fantastic
Quote:

Originally Posted by brumby_3
I still don't know how to do the first question. :S

Where are you stuck? What don't you understand? If you have not yet been taught this material (and that's how it seems) then I don't know why you would be attempting these questions.