Math Problem Solver

Division of one complex number by another

Note that we cannot divide one complex number by another complex number, however we

define the division of a complex number as the elimination of the imaginary number 𝑖 from the

denomination using the conjugate of the denominator.

Example 1.2

Simplify

i. 5+3𝑖

−𝑖

ii. 3+4𝑖

5+2𝑖

i. 5+3𝑖

−𝑖

=

5+3𝑖

−𝑖

×

𝑖

𝑖

=

𝑖 5+3𝑖

𝑖

=

5𝑖+3𝑖

2

−𝑖

2

=

5𝑖−3

𝑖

= 5𝑖 − 3

ii. 3+4𝑖

5+2𝑖

=

3+4𝑖

5+2𝑖

5−2𝑖

5−2𝑖

3 5−2𝑖 + 4𝑖(5−2𝑖)

25+4

15−6𝑖+20𝑖+8

29

23+14𝑖

29