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**Introduction to Complex Numbers**

Adding, Subtracting, Multiplying And Dividing Complex Numbers Describe any number in the complex number system.

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**a + bi Complex Numbers are written in**

the form a + bi, where a is the real part and b is the imaginary part. a + bi real part imaginary part

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**(3 + 7i) + (8 + 11i) 11 + 18i When adding complex numbers,**

add the real parts together and add the imaginary parts together. imaginary part (3 + 7i) + (8 + 11i) real part i

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**When subtracting complex numbers,**

be sure to distribute the subtraction sign; then add like parts. (5 + 10i) – (15 – 2i) 5 + 10i – i – i

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**When multiplying complex numbers,**

use the FOIL method. (3 – 8i)(5 + 7i) i – 40i – 56i2 15 – 19i + 56 Remember, i2 = –1 71 – 19i

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To divide complex numbers, multiply the numerator and denominator by the complex conjugate of the complex number in the denominator of the fraction. 7 + 2i 3 – 5i The complex conjugate of 3 – 5i is 3 + 5i.

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7 + 2i 3 – 5i (3 + 5i) (3 + 5i) i + 6i + 10i2 9 + 15i – 15i – 25i2 i 34 i – 10 9 + 25

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Try These. (3 + 5i) – (11 – 9i) (5 – 6i)(2 + 7i) 2 – 3i 5 + 8i 4. (19 – i) + (4 + 15i)

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Try These. (3 + 5i) – (11 – 9i) i (5 – 6i)(2 + 7i) i 2 – 3i –14 – 31i 5 + 8i 4. (19 – i) + (4 + 15i) i

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Section 8.7 Complex Numbers. Overview In previous sections, it was not possible to find the square root of a negative number using real numbers: is not.

Section 8.7 Complex Numbers. Overview In previous sections, it was not possible to find the square root of a negative number using real numbers: is not.

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