Question

Simplify the following expression: |2+4i|

Answer 1

Answer:

$\sqrt{20}$

Step-by-step explanation:

This is a complex number expression, and you are asked to find the absolute value.

in a complex number, there are two parts, the real and the imaginary part.

in the question ; 2 = real part,   4 = imaginary part

based on the diagram, we will use Pythagoras theorem to solve for the hypotenuse which gives the absolute value of the complex number.

$|2+4i|^{2}$ = $2^{2}$ + $4^{2}$

                              = 4 + 16

                              = 20

  ;                |2+4i|   = $\sqrt{20}$

Answer 2

Use distance formula (Pythagorean theorem) to find the complex number's distance from zero. There is an imaginary axis and a real axis, and these behave very much like the regular x and y axes. √(2² + 4²) = √20 
The absolute value of 2 + 4i is √20