Learn How to Solve Complex Expressions Tutorial - Definition, Formula, Example

Learn How to Solve Complex Expressions - Tutorial

Definition:

When a number in the form a + bi (a real number plus an imaginary number) it is called as complex number. This tutorial will help you to solve complex expressions.

Example1 :

Simplify Complex Numbers: (2+3i)*(4-5i)

Given,

Complex Number 1 ==> (2+3i) Complex Number 2 ==> (4-5i)

Solution:

Step 1:

Complex number 2 is multiplied by 2, 2 * (4-5i) = 8-10i --> 1

Step 2:

Complex number 2 is multiplied by 3i, 3i * (4-5i) = 12i-15i² = 12i + 15 --> 2

where,

i² = -1

By adding 1 and 2 we will get, (2+3i)*(4-5i) = 23 + 2i

Example2 :

Simplify Complex Numbers: (8+i)*(1-2i) / (1+3i)

Given

Complex Number 1 ==> (8+i) Complex Number 2 ==> (1-2i) Complex Number 3 ==> (1+3i)

Solution:

Step 1:

Multiply Complex number 1 and 2,

(8+i)*(1-2i)	= 8(1) + 8(-2i) + i(1) + i(-2i)
	= 8 - 16i + i - 2i²
	= 8 - 15i - 2(-1)
	= 8 - 15i + 2
	= 10 - 15i

Step 2:

Step 1 result divided by Complex number 3,

(10-15i) / (1+3i)	= ((10-15i)(1-3i)) / ((1+3i)(1-3i))
	= (10 -30i - 15i + 45i²) / (1-9i²)
	= (10 -45i + 45(-1)) / (1-9(-1))
	= (10 -45i - 45) / (1+9)
	= (-35 -45i) / 10
	= 5 (-7 -9i) / 10
	= (-7 -9i) / 2
	= -3.5 -4.5i
(8+i)*(1-2i) / (1+3i)	= -3.5 -4.5i

Learn How to Solve Complex Expressions Tutorial - Definition, Formula, Example