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Question: The modulus of \(\frac{1 + 7i}{(2–i)^{2}}\)is –...

The modulus of 1+7i(2–i)2\frac{1 + 7i}{(2–i)^{2}}is –

A

5\sqrt{5}

B

0

C

2\sqrt{2}

D

1

Answer

2\sqrt{2}

Explanation

Solution

Sol. 1+7i4+i2–4i\frac{1 + 7i}{4 + i^{2}–4i} = 1+7i3–4i\frac{1 + 7i}{3–4i}

∣1+7i∣∣3–4i∣\frac{|1 + 7i|}{|3–4i|} = 12+7232+(–4)2\frac{\sqrt{1^{2} + 7^{2}}}{\sqrt{3^{2} + (–4)^{2}}} = 505\frac{\sqrt{50}}{5} = 2\sqrt{2}