Complex numbers (HSC SSCE Mathematics Extension 2): Flashcards

A number of the form z = x + iy, with real x and imaginary y.

Modulus r = √(x² + y²) from the complex number z = x + iy.

The angle θ with the positive real axis, θ = tan⁻¹(y/x).

Add real parts and imaginary parts separately: (a+bi) + (c+di).

(a+bi)(c+di) = (ac - bd) + (ad + bc)i.

The conjugate of z = x + iy is denoted as x - iy.

Use conjugates: (a+bi)/(c+di) = (a+bi)(c-di)/(c²+d²).

z = r(cosθ + isinθ), where r is modulus and θ is argument.

Calculate r = √(x² + y²) and θ = tan⁻¹(y/x).

Used in engineering to evaluate electrical impedance Z = R + iX.