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

english Calculators and Converters

Ask a Question