Introduction to Complex Numbers Adding, Subtracting, Multiplying

Introduction to Complex Numbers Adding, Subtracting, Multiplying And Dividing Complex Numbers SPI 3103.2.1 Describe any number in the complex number system.

Complex Numbers (a bi) Natural (Counting) Numbers bers Whole Num s Integer bers m u N l Rationa bers m u N l a Re at r r I io ’s # l na Imaginary #’s

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

When adding complex numbers, add the real parts together and add the imaginary parts together. imaginary part (3 7i) (8 11i) real part 11 18i

When subtracting complex numbers, be sure to distribute the subtraction sign; then add like parts. (5 10i) – (15 – 2i) 5 10i – 15 2i –10 12i

When multiplying complex numbers, use the distributive property and simplify. (3 – 8i)(5 7i) 15 21i – 40i – 56i 15 – 19i 56 71 – 19i 2 Remember, i2 –1

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.

7 (3 2i 5i) (3 5i) 3 – 5i 21 35i 6i 2 10i 9 15i – 15i – 2 41i – 10 21 25i 9 25 11 41i 34

Try These. 1.(3 5i) – (11 – 9i) 2.(5 – 6i)(2 7i) 3.2 – 3i 5 8i 4. (19 – i) (4 15i)

Try These. 1.(3 5i) – (11 – 9i) 2.(5 – 6i)(2 7i) -8 14i 52 23i 3.2 – 3i 5 8i –14 – 31i 89 4. (19 – i) (4 15i) 23 14i

Investigate the powers of i. Power Exponential form simplified 1 i 0 i 2 i2 -1 3 4 5 6 7 8 9 12 27 70 -10