Complex Numbers · Mathematics · MHT CET

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...

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

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}, ...

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...

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

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

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

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...

The argument of $$\frac{1+i \sqrt{3}}{\sqrt{3}+i}, i=\sqrt{-1}$$ is

If $$w=\frac{z}{z-\frac{1}{3} i}$$ and $$|w|=1, i=\sqrt{-1}$$, then $$z$$ lies on

If $$Z_1=2+i$$ and $$Z_2=3-4 i$$ and $$\frac{\overline{Z_1}}{Z_2}=a+b i$$, then the value of $$-7 a+b$$ is (where $$i=\sqrt{-1}$$ and $$a, b \in R)$$...

If $$Z_1=4 i^{40}-5 i^{35}+6 i^{17}+2, Z_2=-1+i$$, where $$i=\sqrt{-1}$$, then $$\left|Z_1+Z_2\right|=$$

Let $$z$$ be a complex number such that $$|z|+z=3+i, i=\sqrt{-1}$$, then $$|z|$$ is equal to

If $$\omega$$ is the complex cube root of unity, then $$\left(3+5 \omega+3 \omega^2\right)^2+\left(3+3 \omega+5 \omega^2\right)^2=$$

If $$z(2-i)=(3+i)$$, then $$z^{38}=$$, ( where $$z=x+i y$$)

The complex number with argument $$\frac{5 \pi^{\mathrm{c}}}{6}$$ at a distance of 2 units from the origin is

If $$\omega$$ is complex cube root of unity and $$(1+\omega)^7=A+B\omega$$, then values of A and B are, respectively

The value of (1 + i)$$^5$$ (1 $$-$$ i)$$^7$$ is