List of top Mathematics Questions on Complex numbers asked in MHT CET

If two sides of a triangle are \( \sqrt{3} - 1 \) and \( \sqrt{3} + 1 \) units and their included angle is \( 60^\circ \), then the third side of the triangle is

The projection of the line segment joining the points \( (2, 1, -3) \) and \( (-1, 0, 2) \) on the line whose direction ratios are \( 3, 2, 6 \) is

If $y = \log_e x^3 + 3 \sin^{-1} x + kx^2$ and $y'\left(\frac{1}{2}\right) = 2\sqrt{3}$, then $k =$}

The general solution of $x(x - 1)\frac{dy}{dx} = x^3(2x - 1) + (x - 2)y$ is

The equation $|z + 1 - i| = |z - 1 + i|$ represents a (where z is a complex number)

If two sides of a triangle are \( \sqrt{3} - 1 \) and \( \sqrt{3} + 1 \) units and their included angle is \( 60^\circ \), then the third side of the triangle is

The projection of the line segment joining the points \( (2, 1, -3) \) and \( (-1, 0, 2) \) on the line whose direction ratios are \( 3, 2, 6 \) is

If the amplitude of $(z - 2 - 3i)$ is $\frac{3\pi}{4}$, then the locus of $z$ is (where $z = x + iy$)