Topic explanation

Standard explanation

z^2 + 4 = (z+2i)(z-2i). Complete square: z^2 + 2z + 5 = (z+1)^2 + 4 = (z+1)^2 - (2i)^2. Roots come in conjugate pairs if coefficients are real.

Key points

• real coeffs -> conjugate roots
• complex coeffs: still algebra
• z² + a² = (z+ai)(z-ai)
• conjugate pairs
• FACTORS AND QUADRATICS: z^2 + 4 = (z+2i)(z-2i). Complete square: z^2 + 2z + 5 = (z+1)^2 + 4 = (z+1)^2 - (2i)^2. Roots come i
• FACTORS AND QUADRATICS: z² + 4 = (z+2i)(z-2i).
• WHAT — FACTORS AND QUADRATICS: z^2 + 4 = (z+2i)(z-2i). Complete square: z^2 + 2z + 5 = (z+1)^2 + 4 = (z+1)^2 - (2i)^2. Roots come i
• WHY — Why it matters: This rule is a separate learning unit inside linear systems and factorising. It can be defined, appl

Labelled diagram