1
COMEDK 2025 Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $z=\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^5+\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^5$, then
A
$\operatorname{Re}(z)>0, \operatorname{Im}(z)<0$
B
$\operatorname{Im}(z)=0$
C
$\operatorname{Re}(z)=0$
D
$\operatorname{Re}(z)>0, \operatorname{Im}(z)>0$
2
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
The complex number $\frac{1+7 i}{(2-i)^2}$ lies in
A
Quadrant 4
B
Quadrant 3
C
Quadrant 1
D
Quadrant 2
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\frac{x-1}{3+i}+\frac{y-1}{3-i}=i$ then $(y, x)=$
A
$(-6,-4)$
B
$(-4,-6)$
C
$(6,-4)$
D
$(-4,6)$
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If }(1-4 i)^3=a+i b \text { then the value of } \mathrm{a} \text { and } \mathrm{b} \text { is } $$

A
$$-47,52$$
B
$$49,-74$$
C
$$-74,49$$
D
$$-48,-52$$
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