AP EAMCET · Maths · Complex Number
If \(z\) is a complex number such that \(\frac{z-1}{z-i}\) is purely imaginary and locus of \(z\) represents a circle with centre \((\alpha, \beta)\) and radius \(r\), then \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\)
- A \(4 r\)
- B \(r^2\)
- C \(2 r^2\)
- D \(4 r^2\)
Answer & Solution
Correct Answer
(D) \(4 r^2\)
Step-by-step Solution
Detailed explanation
Let \(z = x+iy\). \(Re\left(\frac{z-1}{z-i}\right) = 0\) \(Re\left(\frac{(x-1)+iy}{x+i(y-1)}\right) = 0\) \(\frac{x(x-1) + y(y-1)}{x^2+(y-1)^2} = 0\) \(x^2 - x + y^2 - y = 0\) \(\left(x - \frac{1}{2}\right)^2 + \left(y - \frac{1}{2}\right)^2 = \frac{1}{4} + \frac{1}{4}\)…
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
- If four letters are chosen from the letters of the word ASSIGNMENT and are arranged in all possible ways to form 4 letter words (with or without meaning), then total number of such words that can be formed isAP EAMCET 2025 Medium
- A box contains 6 bottles of \(\mathrm{V}_1\) drink, 3 bottles of \(\mathrm{V}_2\) drink and 4 bottles of \(\mathrm{V}_3\) drink. If three bottles are drawn at random, then the probability that the three are not of the same variety isAP EAMCET 2022 Easy
- If \(\quad d x+d y=(x+y)(d x-d y), \quad\) then \(\log (x+y)\) is equal toAP EAMCET 2005 Easy
- If origin is the ortho-center of an equilateral triangle whose vertices are \(\bar{a}, \bar{b}, \bar{c}\) thenAP EAMCET 2022 Easy
- \(\mathrm{f}(\mathrm{x})\) is differentiable on \(\mathbb{R}\) and \(\mathrm{f}^{\prime}(\mathrm{m}) \neq 0, \mathrm{~m} \in \mathbb{R}\).
If \(\lim _{x \rightarrow m} \frac{x f(m)-m f(x)}{x-m}+f^{\prime}(m)=f(m)\), then \(m=\)AP EAMCET 2023 Medium - If \(A B C D E F\) is a regular hexagon with \(\mathbf{A B}=\mathbf{a}\) and \(\mathbf{B C}=\mathbf{b}\), then \(\mathbf{C E}\) equals toAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- If the vectors \(\mathrm{AB}=-3 \mathbf{i}+4 \mathbf{k}\) and \(\mathrm{AC}=5 \mathbf{i}-2 \mathbf{j}+4 \mathbf{k}\) are the sides of a \(\triangle A B C\), then the length of the median through \(A\) isAP EAMCET 2011 Easy
- For what natural numbers , the inequality is valid?AP EAMCET 2021 Medium
- Which one of the following reactions occur at the anode, in the Castner process of extracting sodium metal ?AP EAMCET 2003 Easy
- \(\int_{-\pi / 2}^{2 \pi} \sin ^{-1}(\sin x) d x=\)AP EAMCET 2022 Medium
- If and are collinear, then the ratio in which divides isAP EAMCET 2020 Easy
- 209 g of an element reacts with chlorine to form 315.5 g of its chloride. What is the weight (in g ) of oxygen that reacts with 418 g of same element?
\((\mathrm{C} \ell=35.5 \mathrm{u} ; \mathrm{O}=16 \mathrm{u})\)AP EAMCET 2025 Medium