1
MHT CET 2023 14th May Morning Shift
+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

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
$$\frac{2}{5}+\frac{4}{5} \mathrm{i}$$
2
MHT CET 2023 13th May Evening Shift
+2
-0

If $$(3 x+2)-(5 y-3) i$$ and $$(6 x+3)+(2 y-4) i$$ are conjugates of each other, then the value of $$\frac{x-y}{x+y}$$ is (where $$\left.i=\sqrt{-1}, x, y \in R\right)$$

A
$$-$$1
B
0
C
1
D
2
3
MHT CET 2023 13th May Morning Shift
+2
-0

The value of $$\frac{\mathrm{i}^{248}+\mathrm{i}^{246}+\mathrm{i}^{244}+\mathrm{i}^{242}+\mathrm{i}^{240}}{\mathrm{i}^{249}+\mathrm{i}^{247}+\mathrm{i}^{245}+\mathrm{i}^{243}+\mathrm{i}^{241}}, (\mathrm{i}=\sqrt{-1})$$ is

A
i
B
1
C
$$-1$$
D
$$-$$i
4
MHT CET 2023 12th May Evening Shift
+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
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