WBJEE · Maths · Complex Number
The modulus of \(\frac{1-i}{3+i}+\frac{4 i}{5}\) is
- A \(\sqrt{5}\) unit
- B \(\frac{\sqrt{11}}{5}\) unit
- C \(\frac{\sqrt{5}}{5}\) unit
- D \(\frac{\sqrt{12}}{5}\) unit
Answer & Solution
Correct Answer
(C) \(\frac{\sqrt{5}}{5}\) unit
Step-by-step Solution
Detailed explanation
\[ \text { Hints: } \frac{1-i}{3+i}+\frac{4 i}{5}=\frac{5-5 i+4 i(3+i)}{5(3+i)}=\frac{5-5 i+12 i-4}{5(3+i)}=\frac{1+7 i}{5(3+i)}=\frac{(1+7 i)(3-i)}{5(9+1)} \] \[ =\frac{3+21 i-i+7}{5 \times 10}=\frac{10+20 i}{5 \times 10}=\frac{1+2 i}{5} \]…
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