# Finding absolute value of imaginary number

• Sep 18th 2011, 09:16 AM
benny92000
Finding absolute value of imaginary number
How do you find the absolute value of 1 plus or minus i. The answer is 1.41
• Sep 18th 2011, 09:20 AM
Plato
Re: Finding absolute value of imaginary number
Quote:

Originally Posted by benny92000
How do you find the absolute value of 1 plus or minus i. The answer is 1.41

$|a+bi|=\sqrt{a^2+b^2}$

so $|\pm a\pm bi|=\sqrt{[\pm a]^2+[\pm b]^2}=\sqrt{a^2+b^2}$
• Sep 18th 2011, 09:20 AM
Prove It
Re: Finding absolute value of imaginary number
Quote:

Originally Posted by benny92000
How do you find the absolute value of 1 plus or minus i. The answer is 1.41

If you were to plot the point $\displaystyle 1 + i$ and draw the length from the origin to that point on an Argand diagram, you'll see that from the origin, you have travelled one unit right and one unit up. So really, a right-angle triangle has been created, with the two shorter sides = 1 unit in length. How would you find the length of the hypotenuse (in other words, $\displaystyle |1 + i|$)?