Complex Numbers: Adding, Subtracting, Multiplying and Dividing, Assignments of Electronic Circuits Design

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Introduction to Complex Numbers 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 Whole Numbers Integers Rational Numbers Real Numbers Irrational #’s Imaginary #’s

When adding complex numbers, add the real parts together and add the imaginary parts together.

(3 + 7i) + (8 + 11i)

real part imaginary part

11 + 18i

When subtracting complex numbers, be sure to distribute the subtraction sign; then add like parts.

(5 + 10i) – (15 – 2i)

• 10 + 12i

5 + 10i – 15 + 2i

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.

2i 3 – 5i 21 + 35i + 6i + 10i 2 9 + 15i – 15i – 25i 2 21 + 41i – 10 9 + 25 (3 + 5i)

5i) 11 + 41i 34

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

4. (19 – i) + (4 + 15i) 23 + 14i

Investigate the powers of i. Power Exponential form simplified 1 i 0+i 2 i 2

3 4 5 6 7 8 9 12 27 70