KCET · Maths · Mathematical Induction
If \(z=x+i y\), then the equation \(|z+1|=|z-1|\) represents
- A a circle
- B a parabola
- C \(X\)-axis
- D \(Y\)-axis
Answer & Solution
Correct Answer
(D) \(Y\)-axis
Step-by-step Solution
Detailed explanation
Given,
\(\begin{gathered}
z=x+i y \\
|z+1|=|z-1| \\
|z+1|^{2}=|z-1|^{2} \\
|x+i y+1|^{2}=|x+i y-1|^{2} \\
(x+1)^{2}+y^{2}=(x-1)^{2}+y^{2} \\
(x+1)^{2}-(x-1)^{2}=0 \\
(x+1-x+1)(x+1+x-1)=0 \\
x=0 \\
\therefore|z+1|=|z-1| \text { represents } Y \text {-axis. }
\end{gathered}\)
\(\begin{gathered}
z=x+i y \\
|z+1|=|z-1| \\
|z+1|^{2}=|z-1|^{2} \\
|x+i y+1|^{2}=|x+i y-1|^{2} \\
(x+1)^{2}+y^{2}=(x-1)^{2}+y^{2} \\
(x+1)^{2}-(x-1)^{2}=0 \\
(x+1-x+1)(x+1+x-1)=0 \\
x=0 \\
\therefore|z+1|=|z-1| \text { represents } Y \text {-axis. }
\end{gathered}\)
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
- Angles of elevation of the top of a tower from three points (collinear) \(A, B\) and \(C\) on a road leading to the foot of the tower are \(30^{\circ}, 45^{\circ}\) and \(60^{\circ}\) respectively. The ratio of \(A B\) to \(B C\) isKCET 2011 Easy
- The degree of the differential equation
\(1+\left(\frac{d y}{d x}\right)^2+\left(\frac{d^2 y}{d x^2}\right)^2=\sqrt[3]{\frac{d^2 y}{d x^2}+1}\) isKCET 2023 Easy - If \(\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{j} - \hat{k}\) and \(\vec{a} \times \vec{c} = \vec{b}, \vec{a} \cdot \vec{c} = 3\), then \(\vec{c}\) isKCET 2026 Medium
- \(\log \left(\sin 1^{\circ}\right) \cdot \log \left(\sin 2^{\circ}\right) \cdot \log \left(\sin 3^{\circ}\right)\) \(\ldots \log \left(\sin 179^{\circ}\right)\)KCET 2013 Easy
- The function \(f(x)=[x]\), where \([x]\) denotes the greatest integer not greater than \(x\), isKCET 2010 Easy
- If the length of the subtangent at any point to the curve \(x y^{n}=a\) is proportional to the abscissa, then \(n\) isKCET 2013 Medium
More PYQs from KCET
- Which of the following statements are correct with reference to single slit diffraction pattern?KCET 2021 Easy
- The law of limiting factors was proposed with particular reference to photosynthesis. Identify the scientist who proposed this law.KCET 2005 Hard
- A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to \(\frac{3}{4}\) of the angle of the prism. The angle of deviation isKCET 2022 Medium
- According to the hypothesis proposed by environmental biologists, a relatively constant environment in tropics promotesKCET 2024 Easy
- A gun fires a small bullet with kinetic energy \(K\). Then kinetic energy of the gun while recoiling isKCET 2013 Easy
- Testa and tegmen of the seed coat representKCET 2019 Easy