List of top Mathematics Questions on Algebra of Complex Numbers asked in MHT CET

A particle P starts from $Z_0 = 1 + 2i$. It moves horizontally away from origin by 5 units, then vertically up by 3 units to $Z_1$. From $Z_1$ it moves $\sqrt{2}$ units in direction $\hat{i} + \hat{j}$, then moves through $\pi/2$ anticlockwise on a circle with centre at origin to reach $Z_2$. Then $Z_2 = \dots$
The modulus of the square root of the complex number $6 + 8i$ (where $i = \sqrt{-1}$) is ______.
Let $z$ be a complex number such that $|z|+z=3+i$ where $i=\sqrt{-1}$, then $|z|=$
If the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \) are \( p \) and \( q \), then what is the value of \( p + q \)?
Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).
The variance of the first 50 even natural numbers is:
The statement \( (p \wedge (\sim q)) \vee ((\sim p) \wedge q) \vee ((\sim p) \wedge (\sim q)) \) is equivalent to:
For a certain function $ u_x $ , given that $ u_0 = 3, u_1 = 12, u_2 = 81, u_3 = 200, u_4 = 100, u_5 = 8 $ , then $ \Delta ^{5}u_{x} $ is equal to