1
JEE Main 2024 (Online) 27th January Morning Shift
+4
-1
If $S=\{z \in C:|z-i|=|z+i|=|z-1|\}$, then, $n(S)$ is :
A
1
B
2
C
3
D
0
2
JEE Main 2023 (Online) 15th April Morning Shift
+4
-1
If the set $\left\{\operatorname{Re}\left(\frac{z-\bar{z}+z \bar{z}}{2-3 z+5 \bar{z}}\right): z \in \mathbb{C}, \operatorname{Re}(z)=3\right\}$ is equal to

the interval $(\alpha, \beta]$, then $24(\beta-\alpha)$ is equal to :
A
36
B
27
C
42
D
30
3
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

Let $$S=\left\{z \in \mathbb{C}: \bar{z}=i\left(z^{2}+\operatorname{Re}(\bar{z})\right)\right\}$$. Then $$\sum_\limits{z \in \mathrm{S}}|z|^{2}$$ is equal to :

A
$$\frac{7}{2}$$
B
4
C
3
D
$$\frac{5}{2}$$
4
JEE Main 2023 (Online) 12th April Morning Shift
+4
-1

Let $$\mathrm{C}$$ be the circle in the complex plane with centre $$\mathrm{z}_{0}=\frac{1}{2}(1+3 i)$$ and radius $$r=1$$. Let $$\mathrm{z}_{1}=1+\mathrm{i}$$ and the complex number $$z_{2}$$ be outside the circle $$C$$ such that $$\left|z_{1}-z_{0}\right|\left|z_{2}-z_{0}\right|=1$$. If $$z_{0}, z_{1}$$ and $$z_{2}$$ are collinear, then the smaller value of $$\left|z_{2}\right|^{2}$$ is equal to :

A
$$\frac{3}{2}$$
B
$$\frac{5}{2}$$
C
$$\frac{13}{2}$$
D
$$\frac{7}{2}$$
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