# Thread: Modulus of complex numbers

1. ## Modulus of complex numbers

So, I wasn't there when they went through this in class, and even though I've looked on the internet, I have no idea what to do.
Help would be greatly appreciated. (:

Find the modulus of the following complex numbers:

3+5i

6-10i

7-8i

(3+5i)^3

2. Originally Posted by Fnus
So, I wasn't there when they went through this in class, and even though I've looked on the internet, I have no idea what to do.
Help would be greatly appreciated. (:

Find the modulus of the following complex numbers:

3+5i

6-10i

7-8i
the modulus of a complex number $\displaystyle z = x + iy$ is given by: $\displaystyle |z| = \sqrt{x^2 + y^2}$

example, find the modulus of $\displaystyle z = 3 + i \sqrt{7}$

$\displaystyle |z| = \sqrt{3^2 + (\sqrt{7})^2} = \sqrt{16} = 4$

that's it

(3+5i)^3
another rule: $\displaystyle |z^n| = |z|^n$

example, find the modulus of $\displaystyle (3 + i \sqrt{7})^3$

Let $\displaystyle z = 3 + i \sqrt{7}$

we want $\displaystyle |z^3|$

now, $\displaystyle |z^3| = |z|^3 = 4^3 = 64$