Complex Numbers Quiz -1
Comprehensive Complex Numbers Quiz
Test your understanding of Complex Numbers, including definition, algebra, modulus, amplitude, and the Argand Diagram.
Complex Numbers Mcq-02
Complex Numbers Quiz Complex Numbers Quiz 1. The value of \( \left(\frac{-1 + i\sqrt{3}}{1 - i}\right)^{30} \) is (a) \(-2^{15}\) (b) \(2^{15}i\) (c) \(-2^{15}i\) (d) \(6^5\) 2. Let \( z=\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^5+\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^5 \). If \(R(z)\) and \(I(z)\) respectively denote the real and imaginary parts of \(z\), then: (a) \(R(z) > 0\) and \(I(z) > 0\) (b) \(I(z) = 0\) (c) \(R(z) 0\) (d) \(R(z) = -3\) 3. Let \(\left(-2-\frac{1}{3}i\right)^3=\frac{x+iy}{27}\), where \(x\) and \(y\) are real numbers, then \(y - x\) equals: (a) -91 (b) -85 (c) 85 (d) 91 4. The least positive integer \(n\) for which \(\left(\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\right)^n = 1\), is (a) 3 (b) 5 (c) 2 (d) 6 5. Let \(\omega\)...
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