Question

If z=2-i√3, then |z⁴| is equal to

• A. 7
• B. √7
• C. 7√7
• D. 49
• E. 49√7

Answer 1

The Correct Option is D

We are given \(z = 2 - i\sqrt{3}\), and we need to find \(|z^4|\).

First, find the modulus of \(z\). The modulus of a complex number \(z = a + bi\) is given by:

\(|z| = \sqrt{a^2 + b^2}\) 

For \(z = 2 - i\sqrt{3}\), we have \(a = 2\) and \(b = -\sqrt{3}\).

Thus, the modulus of \(z\) is:

\(|z| = \sqrt{2^2 + (-\sqrt{3})^2} = \sqrt{4 + 3} = \sqrt{7}\)

Now, use the property of moduli: \(|z^n| = |z|^n\) for any integer \(n\).

Therefore, \(|z^4| = |z|^4\).

We already know that \(|z| = \sqrt{7} \), s\)

\(|z^4| = (\sqrt{7})^4 = 7^2 = 49\)

The answer is 49.