Question Detail
Question
Obtain the modulus of the complex number \(\frac{3-i}{2+2i}\)
Correct Answer
Option C is the correct answer.
Detailed Explanation
|(3-i)/(2+2i)| = |3-i| / |2+2i|. |3-i| = √(3^2+(-1)^2) = √10. |2+2i| = √(2^2+2^2) = √8 = 2√2. So the modulus is √10 / (2√2) = √(10/8) = √(5/4) = √5/2.
Hint
The modulus of a quotient is the quotient of the moduli: |z1/z2| = |z1|/|z2|.