We have |2-4i2+i| = |2-4i||2+i| = 2^2 + (-4)^22^2+1^2 = 205 = 205 = 2.

jmc

algebra junior

Problem

Evaluate

\frac{2 - 4 i}{2 + i}

Solution

We have

\frac{2 - 4 i}{2 + i} = \frac{∣2 - 4 i ∣}{∣2 + i ∣} = \frac{2 ^{2} + ( - 4 ) ^{2}}{2 ^{2} + 1 ^{2}} = \frac{20}{5} = \frac{20}{5} = 2 .

Final answer