Topic explanation

Standard explanation

Re(z) = x. Im(z) = y. Pure imaginary: x = 0, y != 0. Real: y = 0. 0 = 0 + 0i is still in C. Powers of i cycle every 4 (i, -1, -i, 1).

Key points

• Re and Im
• z = x + i y
• equal <-> both parts equal
• R inside C
• NAME THE PARTS: Re(z) = x. Im(z) = y. Pure imaginary: x = 0, y != 0. Real: y = 0. 0 = 0 + 0i is still in C. Powers o
• NAME THE PARTS: Re(z) = x.
• WHAT — NAME THE PARTS: Re(z) = x. Im(z) = y. Pure imaginary: x = 0, y != 0. Real: y = 0. 0 = 0 + 0i is still in C. Powers o
• WHY — Why it matters: This rule is a separate learning unit inside complex numbers recalled. It can be defined, applied, a

Labelled diagram