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If $\mathrm{z}=\frac{\sqrt{3}}{2}+\frac{\mathrm{i}}{2}, \mathrm{i}=\sqrt{-1}$, then $\left(\mathrm{z}^{201}-\mathrm{i}\right)^{8}$ is equal to
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in: Jee Mains
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- 2 weeks, 2 days ago
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Let x and y be real number such that $50\left(\frac{2 \mathrm{x}}{1+3 \mathrm{i}}-\frac{\mathrm{y}}{1-2 \mathrm{i}}\right)=31+17 \mathrm{i}, \mathrm{i}=\sqrt{-1}$. Then the value of 10(x -3y) is
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- 1
- 2 weeks, 2 days ago
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Let z be a complex number such that $|z+2|=|z-2|$ and $\arg \left(\frac{z+3}{z-i}\right)=\frac{\pi}{4}$. Then $|z|^{2}$ is equal to
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- 1
- 2 weeks, 2 days ago
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Let $\mathrm{S}=\left\{\mathrm{z} \in \mathrm{C}: \mathrm{z}^{2}+4 \mathrm{z}+16=0\right\}$. Then $\sum_{\mathrm{z} \in \mathrm{S}}|\mathrm{z}+\sqrt{3} \mathrm{i}|^{2}$ is equal to
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- 1
- 2 weeks, 2 days ago
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Let $\mathrm{z}_{1}, \mathrm{z}_{2} \in \mathrm{C}$ be the distinct solutions of the equation $\mathrm{z}^{2}+4 \mathrm{z}-(1+12 \mathrm{i})=0$.
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- 1
- 2 weeks, 2 days ago
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Let the set of all values of $\mathrm{k} \in \mathrm{R}$ such that the equation $\mathrm{z}(\overline{\mathrm{z}}+2+\mathrm{i})+\mathrm{k}(2+3 \mathrm{i})=0, \mathrm{z} \in \mathrm{C}$, has at least one solution,
Started by:
- 1
- 2 weeks, 2 days ago
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If $\mathrm{z}=\frac{\sqrt{3}}{2}+\frac{\mathrm{i}}{2}, \mathrm{i}=\sqrt{-1}$, then $\left(\mathrm{z}^{201}-\mathrm{i}\right)^{8}$ is equal to
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