1
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$|z-2+i| \leq 2$$, then the difference between the greatest and least value of $$|z|$$ is ________, $$(\mathrm{i}=\sqrt{-1})$$

A
$$2 \sqrt{5}+4$$
B
$$2 \sqrt{5}$$
C
4
D
8
2
MHT CET 2023 12th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$a > 0$$ and $$z=\frac{(1+i)^2}{a+i},(i=\sqrt{-1})$$ has magnitude $$\frac{2}{\sqrt{5}}$$, then $$\bar{z}$$ is equal to

A
$$-\frac{2}{5}+\frac{4}{5} \mathrm{i}$$
B
$$\frac{2}{5}-\frac{4}{5} \mathrm{i}$$
C
$$-\frac{2}{5}-\frac{4}{5} \mathrm{i}$$
D
$$\frac{2}{5}+\frac{4}{5} \mathrm{i}$$
3
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$x=\frac{5}{1-2 \mathrm{i}}, \mathrm{i}=\sqrt{-1}$$, then the value of $$x^3+x^2-x+22$$ is

A
7
B
9
C
17
D
39
4
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{z}=x+\mathrm{i} y$$ and $$\mathrm{z}^{1 / 3}=\mathrm{p}+\mathrm{iq}$$, where $$x, y, \mathrm{p}, \mathrm{q} \in \mathrm{R}$$ and $$\mathrm{i}=\sqrt{-1}$$, then value of $$\left(\frac{x}{\mathrm{p}}+\frac{y}{\mathrm{q}}\right)$$ is

A
$$\mathrm{p}^2-\mathrm{q}^2$$
B
$$4\left(\mathrm{p}^2-\mathrm{q}^2\right)$$
C
$$\mathrm{p}^2+\mathrm{q}^2$$
D
$$4\left(\mathrm{p}^2+\mathrm{q}^2\right)$$
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