JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z\) be a complex number such that \(\left| z \right| + z = 3 + i\) (where \(i = \sqrt { - 1} \)). Then \(\left| z \right|\) is equal to
- A \(\frac{{\sqrt {34} }}{3}\)
- B \(\frac{5}{3}\)
- C \(\frac{{\sqrt {41} }}{4}\)
- D \(\frac{5}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{3}\)
Step-by-step Solution
Detailed explanation
\(z\, = \,x\, + \,iy\) \(\sqrt {{x^2} + {y^2}} \, + \,x\, + \,iy\, = \,3\, + \,i\) \( \Rightarrow \,y = 1\) \(\sqrt {{x^2} + 1} \, + \,x = 3 \Rightarrow {x^2}\, + \,1 = 9 - 6x + {x^2}\) \( \Rightarrow \,x = \frac{4}{3}\) \(|z|\, = \,\sqrt {{x^2}\, + \,{y^2}} \, = \,\frac{5}{3}\)
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