| 2024-06-28 | If \(2 \cos \theta=x+\frac{1}{x}\) and \(2 \cos \varphi=y+\frac{1}{y}\), then .... |
| 2024-06-28 | Let \(a, b, c\) be distinct complex numbers such that \(\frac{a}{1-b}=\frac{b}{1-c}=\frac{c}{1-a.... |
| 2024-06-28 | \(a, b, c\) are real numbers in the polynomial, \(P(z)=2 z^4+a z^3+\) \(b z^2+c z+3\). If two ro.... |
| 2024-06-28 | Let \(i=\sqrt{-1}\). Define a sequence of complex number by \(z_1=0, z_{n+1}=z_n{ }^2+i\) for \(.... |
| 2024-06-28 | Consider \(a z^2+b z+c=0\), where \(a, b, c \in R\) and \(4 a c>b^2\). If \(z_1\) and \(z_2\).... |
| 2024-06-28 | If ' \(p\) ' and ' \(q\) ' are distinct prime numbers, then the number of distinct imaginary num.... |
| 2024-06-28 | If \(\arg \left(\frac{z_1-\frac{z}{|z|}}{\frac{z}{|z|}}\right)=\frac{\pi}{2}\) and \(\left|\frac.... |
| 2024-06-28 | If \(\alpha, \beta\) be the roots of the equation \(u^2-2 u+2=0\) and if \(\cot \theta=x+1\), th.... |
| 2024-06-28 | Let \(z_1, z_2, z_3\) be three points on \(|z|=1\) Let \(\theta_1 \theta_2\), and \(\theta_3\) b.... |
| 2024-06-28 | For how many positive integers ' \(n\) ' less than or equal to 1000 is (sint+icost)n=sin(nt.... |
| 2024-06-28 | Find the sum and product of the complex numbers -3+-2 and 23-i..... |
| 2024-06-28 | If \(|z|=1\) and \(\omega=\frac{z-1}{z+1}(\) where \(z \neq-1)\), the \(\operatorname{Re}(\omega.... |
| 2024-06-28 | The system of equations \(\left.\begin{array}{cc}|z+1-i| & =2 \\ \operatorname{Re}(z) & .... |
| 2024-06-28 | The real part of 11-cosθ+isinθ is equal to .... |
| 2024-06-28 | The square root of \(3-4 i\) is .... |
| 2024-06-28 | \( A=\{x: x \in N \text {, G.C.D. }(x, 36)=1, x<36\}, B=\{y: y \in N\), G.C.D. \((y, 40)=1, y.... |
| 2024-06-28 | Consider \(A_1, A_2, \ldots ., A_{2025}\) be 2025 sets, such that \(A_1 \subset A_2\) \(\subset .... |
| 2024-06-28 | \[\begin{aligned}& \text { If } \mathrm{A}_1 \times \mathrm{A}_2 \times \mathrm{A}_3 \times .... |
| 2024-06-28 | \(A, B, C\) be three sets such that \(n(A)=2, n(B)=3, n(C)=4\).If \(P(X)\) denotes power set of .... |
| 2024-06-28 | Let \(n\) be a positive integer such that \(1 \leq n \leq 1000\). Let \(M_n\) be the number of i.... |
| 2024-06-28 | Consider a set \(S=\left\{a_1^{2025}, a_2^{2025}, a_3^{2025}, \ldots . ., a_n^{2025}\right\}\) a.... |
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