Algebra and Trigonometry III

REAL NUMBER RATIONAL IRRATIONAL INTEGERSNON INTEGERS NEGATIVE …, – 3, – 2, – 1 WHOLE ZERO 0 + Integers Counting or Natural numbers 1, 2, 3, 4, 5, … FRACTION: ½; ¾ 1/3; 2/11 DECIMAL Terminating: 0.5 ; 0.75 Non-terminating : 0.333…; … but repeating DECIMAL: Non-terminating and non-repeating Ex. Radical; Pi; e,, …

PURE IMAGINARY NUMBER COMPLEX NUMBER (a + bi ) REAL NUMBER ( if b=0 )( if a=0 ) Ex. 1) 4 + 0i or 4 2) i or -8 3) 5/7 4) 5) Ex. 1) 0 + 3i or 3i 2) 0 – 5i or – 5i 3) 4i/3 Ex. 1) 5 + 3i 2) – 5 + i 3)

Simplifying i n (simplifying imaginary with exponent higher than 1) From x = 0 x 2 = -1 x = = imaginary To simplify i n, the following will be helpful: i 1 = i i 2 = -1 i 3 = -i i 4 = 1 Examples : 1) i 143 Steps: 1 st. Divide the exponent by 4 (always). 143÷4, the remainder is 3 2 nd. Rewrite the imaginary using the remainder. i 3 3 rd Then simplify using the value at the left. Therefore, i 143 = i 3 = -i 2) -5i 22 = 5 Solution: -5i 34 = -5i 2 = -5(-1)

COMPLEX NUMBER (a + bi ) A. True or False(if false give the reason) 1. Every real number is a complex no. T 2. Every complex number is a real no. F 3. Every irrational no. is a complex no. T 4. Every integer can be written in the form a + bi T 5. Every complex number maybe expressed as an irrational no. F 6. Every negative integer maybe written as a pure imaginary number. F B. Simplify : 7) = -i 8) =1 9) = 5 10) = -7i

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