Strategy 1: Substitute z = x + iy early For equations involving both z and z-bar, immediately write z = x+iy and z-bar = x-iy. Separate real and imaginary parts.

Strategy 2: Use |z|^2 = z * z-bar When you see |z|^2, replace with zz-bar. When you see zz-bar, recognize it as |z|^2. This interconversion is used in almost every problem.

Strategy 3: Polar form for powers/products Any problem involving $z^n$, z1*z2, or z1/z2 is faster in polar form. Convert, operate, convert back.

Strategy 4: Geometry for locus If the equation involves |z - z1|, arg(z - z1), or similar, think geometrically before algebraically.

Strategy 5: Cube roots of unity simplification Whenever w appears, immediately use 1 + w + $w^2$ = 0 and $w^3$ = 1 to reduce expressions. Replace $w^2$ with -1-w or w with -1-$w^2$ as needed.

Strategy 6: Section formula Point dividing z1z2 in ratio m:n internally: z = $\frac{mz2 + nz1}{(m+n)}$. Externally: z = $\frac{mz2 - nz1}{(m-n)}$.

Time allocation: Most JEE complex number problems should be solvable in 2-3 minutes with the right approach.