BRANCH-E&TC ENGINEERING

SEM -3RD

SUBJECT-MATH -3

CHAPTER-01

TOPIC-COMPLEXNUMBER

FACULTY- tapas Ranjan si

Introduction to Complex Numbers

Adding, Subtracting, Multiplying

And Dividing Complex Numbers

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Complex Numbers (a + bi)

Natural (Counting) Numbers

Whole Numbers

Integers

Rational Numbers

Real Numbers

Irrational #’s

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.

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(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.

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(5 + 10i) – (15 – 2i)

–10 + 12i

5 + 10i – 15 + 2i

When multiplying complex numbers,

use the distributive property and simplify.

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(3 – 8i)(5 + 7i)

71 – 19i

15 + 21i – 40i – 56i²

15 – 19i + 56

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.

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7 + 2i

3 – 5i

The complex conjugate of 3 – 5i is 3 + 5i.

7 + 2i

3 – 5i

21 + 35i + 6i + 10i²

9 + 15i – 15i – 25i²

21 + 41i – 10

9 + 25

(3 + 5i)

(3 + 5i)

11 + 41i

34

Try These.

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1. (3 + 5i) – (11 – 9i)

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• (5 – 6i)(2 + 7i)

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• 2 – 3i

5 + 8i

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4. (19 – i) + (4 + 15i)

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Try These.

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1. (3 + 5i) – (11 – 9i) -8 + 14i

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• (5 – 6i)(2 + 7i) 52 + 23i

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• 2 – 3i –14 – 31i

5 + 8i 89

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4. (19 – i) + (4 + 15i) 23 + 14i

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Investigate the powers of i.