AP EAMCET · Maths · Complex Number
If a point \(P\) denotes a complex number \(z=x+i y\) in the argand plane and if \(\frac{z+1}{z+i}\) is a purely real number, then the locus of \(P\) is
- A \(x+y+1=0\)
- B \(x^2+y^2+x+y=0\)
- C \(x^2+y^2+2 y+1=0,(x, y) \neq(0,-1)\)
- D \(x+y+1=0,(x, y) \neq(0,-1)\)
Answer & Solution
Correct Answer
(D) \(x+y+1=0,(x, y) \neq(0,-1)\)
Step-by-step Solution
Detailed explanation
Since \[ \begin{aligned} & \frac{z+1}{z+i}=\frac{x+i y+1}{x+i y+i}=\frac{(x+1)}{x+i(y+1)} \\ & \times \frac{x-i(y+1)}{x-i(y+1)} \end{aligned} \] If \(\frac{z+1}{z+i}\) is a purely real number, \(z \neq-i\)…
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