1. Writing complex numbers Unit 1: topic 3

2. VOCABULARY • Square root: A number r is a square root of a number if r2 = s • Radical: the symbol √ is a radical sign • Radicand: the number beneath the radical sign • Imaginary unit i: defined as • i = √-1 • i2 = -1

3. VOCABULARY • Complex number: written in standard form a + bi • a and b are numbers • a is the real part • b is the imaginary part • Imaginary number • If b ≠ 0, then a+ bi is an imaginary number • Pure imaginary number • If a = 0 and b ≠ 0, then a + bi is a pure imaginary number

4. Properties of square roots • Simplify the expression • Ex1: √8 * √6 • = √48 • = √48 2 24 2 12 2 6 2 3 • = 4√3

5. Properties of square roots • EX 2: √5/36 • EX 3: √300 • EX 4: √20/81

6. Write complex numbers in standard form • Ex1: √-9 • = √9 *√-1 • = 3i • Ex2: √-12 • = √12 * √-1 • = 2√3 * i • = 2i√3 • Ex3: 4 + √-16 • = 4 + √16 * √-1 • = 4 + 4i

7. Equality of Complex Numbers • Ex1: 2x + 2yi = 6 + 4i • Set real parts equal • 2x = 6 • X = 3 • Set imaginary parts equal • 2y = 4 • Y = 2