List of top Statistical Science Questions on Complex Numbers

Let \(Z_1\) and \(Z_2\) be two complex numbers, then:

Let \(Z_1 = -2 + 2i\) and \(Z_2 = 3i\), then:

Let \(x + iy = (2 - i)^2 + \left(\frac{7-4i}{2-i}\right) - 8\), the values of \(x\) and \(y\) are:

Let \(Z_1 = r_1(\cos \theta_1 + i\sin \theta_1)\) and \(Z_2 = r_2(\cos \theta_2 + i\sin \theta_2)\) be two complex numbers, then value of \(Z_1Z_2\) is

If \(\cos \theta = \frac{e^{i\theta} + e^{-i\theta}}{2}\) and \(\sin \theta = \frac{e^{i\theta} - e^{-i\theta}}{2i}\), then \(\cos \theta - i\sin \theta\) is equal to

If A and B be orthogonal matrices of same size, then

Let \(z_1\) and \(z_2\) be two complex numbers, then the dot product of \(z_1\) and \(z_2\) is :

The value of \(\frac{5+5i}{3-4i} + \frac{20}{4+3i}\) is given by :

Let \(z_1\) and \(z_2\) be two complex numbers, then :

Polar form of the complex number \(z = -4 + i4\sqrt{3}\) is :

The equation of a normal to the parabola $y^2 = 4 x$, which passes through the point (9, 6) is :

A line $p x + q y + r = 0$ touches the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Then which of the following statements is true:

Consider the hyperbola $\frac{x^2}{(\cos \theta)^2} - \frac{y^2}{(\sin \theta)^2} = 1$. If $\theta$ changes, which of the following remains constant?}

The value of \(z = \frac{(-1 + i)^4}{(\sqrt{3} + i)^{10}}\) is:

The value of \((\cos 15^\circ + i \sin 15^\circ)^6\) is: