# finding r, absolute value of (sqrt3 + i)

• Jan 1st 2011, 02:09 PM
BugzLooney
finding r, absolute value of (sqrt3 + i)
I was doing some reading through the forum and noticed a question about De Moivre's theorem and realized that I don't know how to find r at all.

I was wondering why the radius is 2 when you take the absolute value of (sqrt3 + i)
• Jan 1st 2011, 02:12 PM
pickslides
For $\displaystyle \displaystyle x+yi \implies r =\sqrt{x^2+y^2}$

so $\displaystyle \displaystyle \sqrt{3}+i \implies r =\sqrt{(\sqrt{3})^2+1^2} =\sqrt{4}=2$
• Jan 1st 2011, 02:27 PM
BugzLooney
Is this the form that all of these types of questions are in? I mean would it be possible to see a question asking for the absolute value of (sqrt3 + i) without any hints of r or anything?
• Jan 1st 2011, 02:29 PM
pickslides
Any question where you need to find the solutions of a complex equation using De Moivre's would assume $\displaystyle r$ is needed.
• Jan 1st 2011, 02:55 PM
Quote:

Originally Posted by BugzLooney
Is this the form that all of these types of questions are in? I mean would it be possible to see a question asking for the absolute value of (sqrt3 + i) without any hints of r or anything?

You could be required to calculate the "modulus" of a complex number.

On an Argand Diagram, a complex number's "modulus" is it's distance from the origin $\displaystyle (0,0)$.

Pythagoras' theorem calculates this
[you can draw a right-angled triangle with hypotenuse being the line from $\displaystyle (0,0)$ to $\displaystyle z$].

$\displaystyle z=a+ib$

$\displaystyle r^2=|z|^2=a^2+b^2\Rightarrow\ |z|=r=\sqrt{a^2+b^2}$
• Jan 1st 2011, 03:15 PM
rtblue
For any further questions you might have, I find this video to be very informative:

YouTube - The Polar Form of Complex Numbers