Defining Complex Numbers Adapted from Walch EducationAdapted
from Walch Education
Slide 3
Important Concepts All rational and irrational numbers are real
numbers. The imaginary unit i is used to represent the non- real
value,. An imaginary number is any number of the form bi, where b
is a real number, i =, and b 0. Real numbers and imaginary numbers
can be combined to create a complex number system. 4.3.1: Defining
Complex Numbers, i, and i 2 2
Slide 4
Complex Numbers All complex numbers are of the form a + bi,
where a and b are real numbers and i is the imaginary unit. In the
general form of a complex number, a is the real part of the complex
number, and bi is the imaginary part of the complex number. if a =
0, the complex number a + bi is wholly imaginary and contains no
real part: 0 + bi = bi. If b = 0, the complex number a + bi is
wholly real and contains no imaginary part: a + (0)i = a. 4.3.1:
Defining Complex Numbers, i, and i 2 3
Slide 5
Important (really) i 0 = 1 i 1 = i i 2 = 1 i 3 = i i 4 = 1
4.3.1: Defining Complex Numbers, i, and i 2 4
Slide 6
Practice Rewrite the radical using the imaginary unit i. 4.3.1:
Defining Complex Numbers, i, and i 2 5
Slide 7
Solution Rewrite the value under the radical as the product of
1 and a positive value. Rewrite the radical as i. 4.3.1: Defining
Complex Numbers, i, and i 2 6
Slide 8
Solution, continued. Rewrite the positive value as the product
of a square number and another whole number. 32 = 16 2, and 16 is a
square number. Simplify the radical by finding the square root of
the square number. 4.3.1: Defining Complex Numbers, i, and i 2
7
Slide 9
Can you Simplify i 57. 4.3.1: Defining Complex Numbers, i, and
i 2 8