Complex Numbers and Quadratic Equations

What is the value of $i^{35}$?

What is the multiplicative inverse of $2 - 3i$?

What is the modulus of the complex number $-1 + i\sqrt{3}$?

What is the conjugate of the complex number $3 - 4i$?

What is the polar form of the complex number $1 + i$?

What are the roots of the quadratic equation $x^2 + x + 1 = 0$?

What is the value of $i^{-39}$?

If $(x + iy)(1 + i) = 2$, then what is the value of $x$ and $y$?

What is the argument of the complex number $-1 - i$?

If $z_1 = 2 - i$ and $z_2 = 1 + i$, what is the value of $\left|\frac{z_1 + z_2 + 1}{z_1 - z_2 + i}\right|$?

What is the real part of the complex number $\frac{1}{1 - i}$?

What are the roots of the quadratic equation $3x^2 - 4x + \frac{20}{3} = 0$?

If $x = -5 + 2\sqrt{-4}$, find the value of $x^4 + 9x^3 + 35x^2 - x + 4$.

If $(1+i)y^2 + (6+i)y + (2+6i) = 0$, what are the possible values of $y$?

What is the multiplicative inverse of $1 + i$?

If $x + iy = \frac{3}{2 + \cos\theta + i\sin\theta}$, then what is the value of $x$?

Express $(1 - i) - (-1 + i6)$ in the form $a + ib$.

What is the value of $\sum_{n=1}^{13} (i^n + i^{n+1})$?

If $(a + ib) = \frac{x + i}{x - i}$, where $x$ is real, what is the value of $a^2 + b^2$?

What is the principal argument of $z = -i$?