JEE Main 2025 PYQ: z1 and z2 satisfy |z1-8-2i|≤1 and |z2-2+6i|≤2. Find the minimum value of |z1-z2| by interpreting the inequalities as two disjoint circular discs.
JEE Main 2024 PYQ: given z1+z2=5 and z1³+z2³=20+15i, find |z1⁴+z2⁴| by working through z1z2, then z1²+z2², using the standard algebraic identities.
JEE Main 2025 PYQ: |z-i|/|2z+i|=1/3 traces a circle with center C. Given the triangle (0,0), C, (α,0) has area 11, find α² using the circle equation and area formula.
JEE Main 2025 PYQ: k1 and k2 are chosen randomly from the natural numbers — find the probability that i^k1+i^k2 is non-zero, using the 4-cycle of powers of i.
The locus |z/(z+i)|=2 in the complex plane is a circle with centre P. Find the distance of P from the point D(1,5) by converting to Cartesian form.
JEE Main 2025 PYQ: find alpha squared given that |(z-bar – i)/(2z-bar + i)| = 1/3 is a circle with centre C, and the triangle with vertices origin, C, (alpha,0) has area 11.
Find the locus of (x,y) given Re((z-1)/(2z+i))=1 for z=x+iy, by rationalising the fraction and simplifying its real part into a circle equation.
Given z1,z2,z3 on |z|=1 with arg(z1)=−π/4, arg(z2)=0, arg(z3)=π/4, find α²+β² where |z1z̄2+z2z̄3+z3z̄1|²=α+β√2.
Find the sum of all possible values of θ ∈ [-π, 2π] for which (1+i cosθ)/(1-2i cosθ) is purely imaginary. Multiple-choice: 3π, 2π, 5π, or 4π.
Find the sum of the squares of the modulus of complex numbers z=a+ib (a,b integers) satisfying |z−1|≤1 and |z−5|≤|z−5i|, by finding the disk and half-plane the condition defines.