TS EAMCET · Maths · Complex Number
If the eight vertices of a regular octagon are given by the complex numbers \(\frac{1}{x_{\mathrm{j}}-2 i}(\mathrm{j}=1,2,3,4,5,6,7,8)\), then the radius of the circumcircle of the octagon is
- A \(\frac{1}{4}\)
- B \(\frac{1}{4}i\)
- C i
- D 2
Answer & Solution
Correct Answer
(A) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
Let the vertices of the octagon be \(z_{\mathrm{j}}\). So, \(z_{\mathrm{j}} = \frac{1}{x_{\mathrm{j}}-2i}\). Let \(w_{\mathrm{j}} = x_{\mathrm{j}}-2i\). Then \(z_{\mathrm{j}} = \frac{1}{w_{\mathrm{j}}}\). The points \(w_{\mathrm{j}}\) lie on the line \( \mathrm{Im}(w) = -2 \).…
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
- Let \(x=\left\{\left[\begin{array}{ll}a & b \ c & d\end{array}\right]: a, b, c, d \in \mathbb{R}\right\}\). If \(f: X \rightarrow \mathbb{R}\) is defined by \(\mathrm{f}(\mathrm{A})=\operatorname{det}(\mathrm{A}) \forall \mathrm{A} \in \mathrm{X}\), then \(\mathrm{f}\) isTS EAMCET 2023 Easy
- If \(f: R \rightarrow R\) is defined by \(f(x)=\left\{\begin{array}{ccc} \frac{x+2}{x^2+3 x+2} & \text { if } & x \in R-\{-1,-2\} \ -1 & \text { if } & x=-2 \ 0 & \text { if } & x=-1 \end{array}\right.\) then \(f\) is continuous on the setTS EAMCET 2005 Medium
- If the point of intersection of the lines \(\mathbf{r}=\hat{\mathbf{i}}-6 \hat{\mathbf{j}}+(p \sec \alpha) \hat{\mathbf{k}}+t(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}})\) and \(\mathbf{r}=4 \hat{\mathbf{j}}+\hat{\mathbf{k}}+\lambda(2 \hat{\mathbf{i}}+(p \tan \alpha) \hat{\mathbf{j}}+2 \hat{\mathbf{k}})\) is \(8 \hat{\mathbf{i}}+8 \hat{\mathbf{j}}+9 \hat{\mathbf{k}}\), (where \(0 < \alpha < \frac{\pi}{2}\) ), then \(p=\)TS EAMCET 2020 Easy
- The perimeter of the triangle with vertices at \((1,0,0),(0,1,0)\) and \((0,0,1)\) isTS EAMCET 2009 Easy
- In a game of throwing 3 coins, a player will loose ₹ \(5 /\) - for each head and gain ₹ 10 - for each tail. If a random variable \(X: S \rightarrow R\) is defined as \(X(a)=\) net gain \((a \in S)\), then the mean of the random variable is (in rupees)TS EAMCET 2018 Medium
- Let be the position vector of a point . Let be a point on the line which is passing through and parallel to the vector . If , then the position vector of isTS EAMCET 2018 Easy
More PYQs from TS EAMCET
- Consider the following reactions \(\begin{aligned} & \mathrm{Cs}+\mathrm{O}_2 \text { (excess) } \rightarrow \mathrm{X} \ & \mathrm{Na}+\mathrm{O}_2 \rightarrow \mathrm{Y} \end{aligned}\)
Identify the correct statement about \(X\) and \(Y\)TS EAMCET 2024 Medium - If the function defined by \(f(x)=\left\{\begin{array}{cl}\frac{2^x-2^{-x}}{x}, & x \neq 0 \text { is continuous at } \ k, & x=0\end{array}\right.\) \(x=0\), then \(e^k\) is equal toTS EAMCET 2021 Easy
- Two vibrating strings ' ' and ' ' produce beats of frequency . The beat frequency is found to reduce to if the tension in the string is slightly reduced. If the original frequency of is , then the frequency of ' isTS EAMCET 2021 Medium
- 100 mL of \(0.05 \mathrm{M} \mathrm{Cu}^{2+}\) aqueous solution is added to 1 L of 0.1 M KI solution. The number of moles of \(\mathrm{I}_2\) and \(\mathrm{Cu}_2 \mathrm{I}_2\) formed are respectivelyTS EAMCET 2025 Medium
- \(\overrightarrow{\mathbf{a}} \cdot \hat{\mathbf{i}}=\overrightarrow{\mathbf{a}} \cdot(2 \hat{\mathbf{i}}+\hat{\mathbf{j}})=\overrightarrow{\mathbf{a}}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}})=1\), then \(\overrightarrow{\mathbf{a}}\) is equal to :TS EAMCET 2006 Easy
- The solution set of the inequation isTS EAMCET 2019 Easy