Chapter 5: Complex Numbers and Quadratic Equations
Q1. Find the modulus and argument of z = 1 + i.
Solution|z| = √(1+1) = √2
arg(z) = tan⁻²(1/1) = π/4
Q2. Solve: x² + 4 = 0.
Solutionx² = -4 = 4i²
x = ±2i
Q3. Express (-1 + i√3) in polar form.
Solutionr = √(1+3) = 2
θ = π - π/3 = 2π/3
z = 2(cos 2π/3 + i sin 2π/3) = 2ei2π/3