AP EAMCET · Maths · Complex Number
The locus of the variable point \(\mathrm{z}=\mathrm{x}+\mathrm{iy}\) whose amplitude is always equal to \(\theta\), is
- A \(\mathrm{x}^2+\mathrm{y}^2=\tan ^2 \theta\)
- B \(y=x \tan \theta\)
- C \(\frac{x^2}{\sin ^2 \theta}+\frac{y^2}{\cos ^2 \theta}=1\)
- D \(\frac{x^2}{\sin ^2 \theta}-\frac{y^2}{\cos ^2 \theta}=1\)
Answer & Solution
Correct Answer
(B) \(y=x \tan \theta\)
Step-by-step Solution
Detailed explanation
Given \(\arg (z)=\theta=\tan ^{-1}\left(\frac{y}{x}\right) \Rightarrow \frac{y}{x}=\tan \theta\) \(\Rightarrow y=x \tan \theta\)
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