List of top Mathematics Questions on Complex Numbers and Quadratic Equations asked in MHT CET

If \(z\) be a complex number such that \( |z| + z = 2 + i \), then find the value of \( |z| \).

If $n \in \mathbb{Z}$, then the expression $\frac{2^n}{(1-i)^{2n}} + \frac{(1+i)^{2n}}{2^n}$ is equal to:

If $n \in \mathbb{Z}$, then the expression $\frac{2^n}{(1-i)^{2n}} + \frac{(1+i)^{2n}}{2^n}$ is equal to:

If $\frac{z-1}{2z+1}$ is an imaginary number and if it represents a circle then its radius is

The area of the triangle whose vertices are $( i, \omega, \omega^2 )$ is (Where $\omega$ is a complex cube root of unity other than 1, $i$ is an imaginary number)________ sq.units

The area of the triangle whose vertices are $( i, \omega, \omega^2 )$ is (Where $\omega$ is a complex cube root of unity other than 1, $i$ is an imaginary number)________ sq.units

If $\frac{z-1}{2z+1}$ is an imaginary number and if it represents a circle then its radius is

The area of the triangle whose vertices are $( i, \omega, \omega^2 )$ is (Where $\omega$ is a complex cube root of unity other than 1, $i$ is an imaginary number)________ sq.units

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

Let $z \in C$ with $\text{Im}(z) = 10$ and it satisfies $\frac{2z-n}{2z+n} = 2i - 1$, $i = \sqrt{-1}$ for some natural number $n$, then}

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

The equation \( x^{3} + x - 1 = 0 \) has