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Question

Question: \[\left| (1 + i)\frac{(2 + i)}{(3 + i)} \right| =\]...

∣(1+i)(2+i)(3+i)∣=\left| (1 + i)\frac{(2 + i)}{(3 + i)} \right| =

A

-1/2

B

½

C

1

D

– 1

Answer

1

Explanation

Solution

Sol. z=(1+i)(2+i)(3+i)=1+3i3+i×3−i3−i=3+4i5⇒∣z∣=1z = \frac{(1 + i)(2 + i)}{(3 + i)} = \frac{1 + 3i}{3 + i} \times \frac{3 - i}{3 - i} = \frac{3 + 4i}{5} \Rightarrow |z| = 1

Trick : ∣z∣=∣z1∣∣z2∣∣z3∣=2.510=1|z| = \frac{|z_{1}||z_{2}|}{|z_{3}|} = \frac{\sqrt{2}.\sqrt{5}}{\sqrt{10}} = 1