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Writing complex numbers

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Writing complex numbers

Unit 1: topic 3

- 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

- 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

- Simplify the expression
- Ex1: √8 * √6
- = √48
- = √48
2 24

2 12

2 6

2 3

- = 4√3

- Ex1: √8 * √6

- EX 2: √5/36
- EX 3: √300
- EX 4: √20/81

- Ex1: √-9
- = √9 *√-1
- = 3i

- Ex2: √-12
- = √12 * √-1
- = 2√3 * i
- = 2i√3

- Ex3: 4 + √-16
- = 4 + √16 * √-1
- = 4 + 4i

- Ex1: 2x + 2yi = 6 + 4i
- Set real parts equal
- 2x = 6
- X = 3
- Set imaginary parts equal
- 2y = 4
- Y = 2