Question

Simplify the following expression:
|2+4i|

Answer 1

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

Answer 2

`√(20)`

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| =
`√(20)`