Verified Answer :

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

Algorithm

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|   = \(\sqrt{20}\)

View image Algorithm

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