Browse · MATH

jmc

algebra junior

Problem

Evaluate

∣2 - 4 i ∣ + ∣2 + 4 i ∣.

Solution

We have

∣2 - 4 i ∣ = 2^{2} + (- 4)^{2} = 20 = 25

. Similarly, we have

∣2 + 4 i ∣ = 2^{2} + 4^{2} = 25

, so

∣2 - 4 i ∣ + ∣2 + 4 i ∣ = 45

.

Final answer

4\sqrt{5}