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JEE Mains · Maths · STD 11 - 4.1 complex nubers
If a complex number \(z\) statisfies the equation \(x + \sqrt 2 \,\,\left| {z + 1} \right|\,+ \,i\, = \,0,\) then \(\left| z \right|\) is equal to
- A \(2\)
- B \(\sqrt 3\)
- C \(\sqrt 5\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(\sqrt 5\)
Step-by-step Solution
Detailed explanation
Given equation is \(z+\sqrt{2}|z+1|+i=0\) put \(z=x+i y\) in the given equation. \((x+i v)+\sqrt{2}|x+i y+1|+i=0\) \(\Rightarrow x+i y+\sqrt{2}[\sqrt{(x+1)^{2}+y^{2}}]+i=0\) Now, equating real and imaginary part, we get \(x+\sqrt{2} \sqrt{(x+1)^{2}+y^{2}}=0\) and…
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