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MCQ (Single Correct Answer)

MHT CET 2023 14th May Evening Shift
Let $$z \in C$$ with $$\operatorname{Im}(z)=10$$ and it satisfies $$\frac{2 z-n}{2 z+n}=2 i-1, i=\sqrt{-1}$$ for some natural number $$\mathrm{n}$$, t...
MHT CET 2023 14th May Morning Shift
If $$a>0$$ and $$z=\frac{(1+i)^2}{a-i}, i=\sqrt{-1}$$, has magnitude $$\frac{2}{\sqrt{5}}$$, then $$\bar{z}$$ is
MHT CET 2023 13th May Evening Shift
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 $$\left.i=\sqrt{-1}, ...
MHT CET 2023 13th May Morning Shift
The value of $$\frac{\mathrm{i}^{248}+\mathrm{i}^{246}+\mathrm{i}^{244}+\mathrm{i}^{242}+\mathrm{i}^{240}}{\mathrm{i}^{249}+\mathrm{i}^{247}+\mathrm{i...
MHT CET 2023 12th May Evening Shift
If $$|z-2+i| \leq 2$$, then the difference between the greatest and least value of $$|z|$$ is ________, $$(\mathrm{i}=\sqrt{-1})$$
MHT CET 2023 12th May Morning Shift
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
MHT CET 2023 11th May Evening Shift
If $$x=\frac{5}{1-2 \mathrm{i}}, \mathrm{i}=\sqrt{-1}$$, then the value of $$x^3+x^2-x+22$$ is
MHT CET 2023 11th May Morning Shift
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 $$\mathr...
MHT CET 2023 10th May Evening Shift
The argument of $$\frac{1+i \sqrt{3}}{\sqrt{3}+i}, i=\sqrt{-1}$$ is
MHT CET 2023 10th May Morning Shift
If $$w=\frac{z}{z-\frac{1}{3} i}$$ and $$|w|=1, i=\sqrt{-1}$$, then $$z$$ lies on
MHT CET 2023 9th May Evening Shift
If $$Z_1=2+i$$ and $$Z_2=3-4 i$$ and $$\frac{\overline{Z_1}}{\overline{Z_2}}=a+b i$$, then the value of $$-7 a+b$$ is (where $$i=\sqrt{-1}$$ and $$a, ...
MHT CET 2023 9th May Morning Shift
If $$Z_1=4 i^{40}-5 i^{35}+6 i^{17}+2, Z_2=-1+i$$, where $$i=\sqrt{-1}$$, then $$\left|Z_1+Z_2\right|=$$
MHT CET 2022 11th August Evening Shift
Let $$z$$ be a complex number such that $$|z|+z=3+i, i=\sqrt{-1}$$, then $$|z|$$ is equal to
MHT CET 2021 24th September Evening Shift
If $$\mathrm{\frac{3+2i}{1+i}=\frac{1}{2}(x+iy)}$$, then x $$-$$ y =
MHT CET 2021 24th September Morning Shift
The sqaure roots of the complex number $$(-5-12 \mathrm{i})$$ are
MHT CET 2021 23rd September Evening Shift
If amplitude of $$(z-2-3 i)$$ is $$\frac{3 \pi}{4}$$, then locus of $$z$$ is (where $$z=x+i y$$)
MHT CET 2021 23th September Morning Shift
If $$z=x+iy$$ satisfies the condition $$|z+1|=1$$, then $$z$$ lies on the
MHT CET 2021 22th September Evening Shift
If $$\omega$$ is the complex cube root of unity, then $$\left(3+5 \omega+3 \omega^2\right)^2+\left(3+3 \omega+5 \omega^2\right)^2=$$
MHT CET 2021 22th September Morning Shift
If $$x=1+2 i$$, then the value of $$x^3+7 x^2-x+16$$ is
MHT CET 2021 21th September Evening Shift
If $$z(2-i)=(3+i)$$, then $$z^{38}=$$, ( where $$z=x+i y$$)
MHT CET 2021 21th September Morning Shift
The complex number with argument $$\frac{5 \pi^{\mathrm{c}}}{6}$$ at a distance of 2 units from the origin is
MHT CET 2021 20th September Evening Shift
If $$\omega$$ is complex cube root of unity and $$(1+\omega)^7=A+B\omega$$, then values of A and B are, respectively
MHT CET 2021 20th September Morning Shift
The value of (1 + i)$$^5$$ (1 $$-$$ i)$$^7$$ is
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