JEE Main 2024 (Online) 29th January Morning Shift | Complex Numbers Question 20 | Mathematics

If $$z=\frac{1}{2}-2 i$$ is such that $$|z+1|=\alpha z+\beta(1+i), i=\sqrt{-1}$$ and $$\alpha, \beta \in \mathbb{R}$$, then $$\alpha+\beta$$ is equal to

$$-$$4

$$-$$1

JEE Main 2024 (Online) 27th January Morning Shift

MCQ (Single Correct Answer)

-1

If $S=\{z \in C:|z-i|=|z+i|=|z-1|\}$, then, $n(S)$ is :

JEE Main 2023 (Online) 15th April Morning Shift

MCQ (Single Correct Answer)

-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 :

JEE Main 2023 (Online) 13th April Evening Shift

MCQ (Single Correct Answer)

-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 :

$$\frac{7}{2}$$

$$\frac{5}{2}$$

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