Complex Numbers · Mathematics · NDA

If $z$ is any complex number and $iz^2 + z - z + i = 0$, where $i = \sqrt{-1}$, then what is the value of $(|z| + 1)^2$?

If $x, y$ and $z$ are the cube roots of unity, then what is the value of $xy + yz + zx$?

Let $z_1$ and $z_2$ be two complex numbers such that $\left|\frac{z_1 + z_2}{z_1 - z_2}\right| = 1$, then what is $\operatorname{Re} \left(\frac{z_1}{...

If $\omega \neq 1$ is a cube root of unity, then what are the solutions of $(z-100)^3 + 1000 = 0$?

What is $(1 + i)^4 + (1 - i)^4$ equal to, where $i=\sqrt{-1}$?

If z z̅ = |z + z̅ |, where z = x + iy, i = $\sqrt{-1}$, then the locus of z is a pair of:

What is the value of $\sqrt{12+5 i}+\sqrt{12-5 i}$ where $i=\sqrt{-1}$ ?

Which one of the following is a square root of $-\sqrt{-1} $?

What are the roots of equation-I ?

Which one of the following is a root of equation-II?

What is the number of common roots of equation-I and equation-II?

If ω is a non-real cube root of 1, then what is the value of  $\left|\frac{1-\omega}{\omega+\omega^2}\right| ?$...

If α and β are the distinct roots of equation x2 - x + 1 = 0, then what is the value of $\left|\frac{\alpha^{100}+\beta^{100}...

If 2 - i√3 where i = √-1 is a root of the equation x2 + ax + b = 0, then what is the value of (a + b)? ...

If $z=\frac{1+i √{3}}{1-i √{3}}$ where i = √-1 then what is the argument of z ?

If z is a complex number such that $\frac{z-1}{z+1}$ is purely imaginary, then what is |z| equal to ?