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

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

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:

The locus of the points represented by \( |z + 3| - |z - 3| = 6 \), where \( z \) is a complex number, is ....

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

If $z = x + iy$ satisfies the condition $|z + 1| = 1$, then $z$ lies on the

The square roots of the complex number $(-5 - 12i)$ are

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

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

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

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

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