Table of Contents

Complex Numbers: Dividing

and write the result in standard form.

Example: Divideii

223

,22223

iiii

First, multiply the numerator and denominator by the complex conjugate of the denominator. (Recall the complex conjugate of a + bi is a – bi.)

,4

24362

2

iiii

,)1(4

)1(276

i

574 i

Here, the complex conjugate of 2 + i is 2 – i.

Table of Contents

Complex Numbers: Dividing

Slide 2

Now, write the result in standard form (a + bi, where a and b are real numbers).

Here 5

74 ibecomes .

57

54

i

Try to divide ,34

2i

i

and write the result in standard form.

The result is, .258

256

i

Table of Contents

Complex Numbers: Dividing

Slide 3

Notes: If the denominator is a pure imaginary number, say 3i, then it is not necessary to multiply the numerator and denominator by the complex conjugate which would be - 3i here. Instead, it is quicker to multiply the numerator and denominator by just i since this will result in i2 in the denominator, hence the "disappearance” of i from the denominator.

ii

43

For example, becomes

.43

41

413

43

43

2

2

ii

iii

iiii

Table of Contents

Complex Numbers: Dividing