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1
KCET 2026
MCQ (Single Correct Answer)
+1
-0
$\sum\limits_{n=1}^{4} (-1)^{2n} \cdot i^{2n} = $
A
$2$
B
$-i$
C
$0$
D
$i$
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0

If $Z_1$ and $Z_2$ are two non-zero complex numbers, then which of the following is not true?

A
$\overline{Z_1+Z_2}=\bar{Z}_1+\bar{Z}_2$
B
$\left|Z_1 Z_2\right|=\left|Z_1\right| \cdot\left|Z_2\right|$
C
$\overline{\mathrm{Z}_1 \mathrm{Z}_2}=\overline{\mathrm{Z}}_1 \cdot \overline{\mathrm{Z}}_2$
D
$\left|\mathrm{Z}_1+\mathrm{Z}_2\right| \geq\left|\mathrm{Z}_1\right|+\left|\mathrm{Z}_2\right|$
3
KCET 2024
MCQ (Single Correct Answer)
+1
-0

The real value of ' $\alpha$ ' for which $\frac{1-i \sin \alpha}{1+2 i \sin \alpha}$ is purely real is

A
$(n+1) \frac{\pi}{2}, n \in N$
B
$(2 n+1) \frac{\pi}{2}, n \in N$
C
$n \pi, n \in N$
D
$(2 n-1) \frac{\pi}{2}, n \in N$
4
KCET 2023
MCQ (Single Correct Answer)
+1
-0

The modulus of the complex number $$\frac{(1+i)^2(1+3 i)}{(2-6 i)(2-2 i)}$$ is

A
$$\frac{2}{\sqrt{2}}$$
B
$$\frac{1}{\sqrt{2}}$$
C
$$\frac{\sqrt{2}}{4}$$
D
$$\frac{4}{\sqrt{2}}$$
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