Modulus of 3+2i3−2i is

3+2i3−2i=3+2i3−2i3+2i3+2i=9−4+12i13=513+i1213Modulus (513)2+(1213)2=1

Modulus of 3+2i3−2i is

3+2i3−2i=3+2i3−2i3+2i3+2i=9−4+12i13=513+i1213Modulus (513)2+(1213)2=1

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Modulus of $(\frac{3 + 2 i}{3 - 2 i})$ is

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1/2

$\sqrt{2}$

answer is A.

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Detailed Solution

$(\frac{3 + 2 i}{3 - 2 i}) = (\frac{3 + 2 i}{3 - 2 i}) (\frac{3 + 2 i}{3 + 2 i}) = \frac{9 - 4 + 12 i}{13} = \frac{5}{13} + i (\frac{12}{13})$

Modulus $\sqrt{{(\frac{5}{13})}^{2} + {(\frac{12}{13})}^{2}} = 1$

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Modulus of $(\frac{3 + 2 i}{3 - 2 i})$ is