8.8 Complex Numbers

# 8.8 Complex Numbers - i n = 1 if the remainder is 1 i n = i...

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8.8 Complex Numbers The complex number system enables us to take even roots of negative numbers by means of the imaginary unit i , which is equal to the square root of –1; that is i 2 = -1 and i = 1 - . By factoring –1 out of a negative expression, it becomes positive and an even root can be taken: -b = i b . Standard form for complex expression is a + bi , where a is the real part and bi is the imaginary part. All properties of exponents hold when the base is i , thus i 1 = i, i 2 = -1, i 3 = i 2 (i) = -1i = -i, i 4 = i 2 (i 2 ) = -1(-1) = 1. In general, for i n , divide n by 4: if the remainder is 0,

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Unformatted text preview: i n = 1 ; if the remainder is 1, i n = i , if the remainder is 2, i n = -1 ; if the remainder is 3, i n = -i. Write in a + bi form: 1. 25-2. a. 50-b.-50 3. 3 16 2-+ Add or subtract: 4. (-1 + 6i) + (5 – 4i) 5. (-5 + i) - (-5 – i) 6. (-6 + 4i) - (2 – i) + (7 – 3i) Multiply: 7. 2 10- × -8. 4(1 – 3 i ) 9. -5 i (2 + 3 i ) 10. (3 - 2 i)(2 – 5i) 11. (4 + 3 i) 2 12. (2 + 6i)(2 – 6i) Divide: 13. 2 8-14. i i-+ 2 5 3 15. i i 3 6 5-...
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