Question

Find the modulus of the complex number 6-2i

Answer 1

Answer:

The modulus of the complex number 6-2i is:

$|z|\:=2\sqrt{10}$

Step-by-step explanation:

Given the number

$6-2i$

We know that

$z = x + iy$

where x and y are real and $\sqrt{-1}=i$

The modulus or absolute value of z is:

$|z|\:=\sqrt{x^2+y^2}$

Therefore, the modulus of $6-2i$  will be:

$z=6-2i$

$z=6+(-2)i$

$|z|\:=\sqrt{x^2+y^2}$

$|z|\:=\sqrt{6^2+\left(-2\right)^2}$

    $=\sqrt{6^2+2^2}$

    $=\sqrt{36+4}$

    $=\sqrt{40}$

    $=\sqrt{2^2}\sqrt{2\cdot \:5}$

    $=2\sqrt{2\cdot \:5}$

   $=2\sqrt{10}$

Therefore, the modulus of the complex number 6-2i is:

$|z|\:=2\sqrt{10}$