Question

The modulus of the complex number \( (2\sqrt{2} + i2\sqrt{2})^2 \) is equal to

• A. \(64 \)
• B. \(4 \)
• C. \(32 \)
• D. \(8 \)
• E. \(16 \)

Hint:

Always simplify modulus first, then apply exponent rule \( |z^n| = |z|^n \).

Answer 1

Answer: (E)

Concept: \[ |z^n| = |z|^n \]

Step 1: Find modulus of base.
\[ z = 2\sqrt{2} + i2\sqrt{2} \] \[ |z| = \sqrt{(2\sqrt{2})^2 + (2\sqrt{2})^2} = \sqrt{8 + 8} = \sqrt{16} = 4 \]

Step 2: Apply power property.
\[ |z^2| = |z|^2 = 4^2 = 16 \]