AP EAMCET · Maths · Complex Number
Let the locus of a point \(\mathrm{z}\) in the Argand plane satisfying the condition \(\operatorname{Re}\left(\mathrm{z}^2\right)=4\) be \(\mathrm{C}_1\) and the locus of \(z\) satisfying the condition \(\operatorname{Im}\left(\mathrm{z}^2\right)=4\) be \(\mathrm{C}_2\). Then the number of common points of the two curves \(\mathrm{C}_1\) and \(\mathrm{C}_2\) are
- A \(0\)
- B \(3\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
Let \(z=x+i y \Rightarrow z^2=x^2-y^2+i 2 x y\) \(\begin{aligned} & \operatorname{Re}\left(z^2\right)=x^2-y^2=4 ..(i)\\ & \operatorname{Im}\left(z^2\right)=2 x y=4 \Rightarrow x y=2 ...(ii)\end{aligned}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- In \(\triangle A B C\), if \(A, B, C\) are in arithmetic progression then
\(\sqrt{\mathrm{a}^2-\mathrm{ac}+\mathrm{c}^2} \cdot \cos \left(\frac{\mathrm{~A}-\mathrm{C}}{2}\right)=\)AP EAMCET 2025 Medium - If \(\int \frac{d x}{2 \cos x+3 \sin x+4}=\frac{2}{\sqrt{3}} f(x)+c\), then \(f\left(\frac{2 \pi}{3}\right)=\)AP EAMCET 2025 Medium
- The locus of \(z\) satisfying the inequality \(\left|\frac{z+2 i}{2 z+i}\right| < 1\), where \(z=x+i y\), isAP EAMCET 2009 Medium
- Variance of the following discrete frequency distribution is
Class Interval 0–2 2–4 4–6 6–8 8–10 Frequency 2 3 5 3 2 AP EAMCET 2025 Medium - For \(x \lt 0, \frac{d}{d x}\left[|x|^x\right]=\)AP EAMCET 2024 Easy
- The solution of the differential equation \(x \frac{d y}{d x}=y-x \tan \left(\frac{y}{x}\right)\) is (Here, \(k\) is an arbitrary constant)AP EAMCET 2019 Medium
More PYQs from AP EAMCET
- Which of the following types of isomerism is exhibited by
\[
\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{NO}_2\right)\right]\left(\mathrm{NO}_3\right)_2
\]
i. Optical ii. Linkage iii. Ionization
iv. CoordinationAP EAMCET 2023 Medium - The reaction of benzene diazonium chloride with Cu and HCl is known asAP EAMCET 2025 Easy
- Assertion : The work done by the electrostatic force is zero when a point charge moves in a circular path around another charge. Reason : The dot product of force and displacement vectors gives work done.AP EAMCET 2019 Easy
- The inverse of the point \((1,2)\) with respect to the circle \(x^2+y^2-4 x-6 y+9=0\), isAP EAMCET 2008 Medium
- If a charged particle enters a uniform magnetic field normally with certain velocity, then the time period of revolution of the particleAP EAMCET 2025 Easy
- If \(y=\frac{\sin \mathrm{h}^{-1} x}{\sqrt{1+x^2}}\), then \(\left(1+x^2\right) \mathrm{y}_2+3 \mathrm{xy}_1+\mathrm{y}=\)AP EAMCET 2017 Medium