Defining Complex Numbers Adapted from Walch EducationAdapted from Walch Education

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 : Defining Complex Numbers, i, and i 2 2

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 : Defining Complex Numbers, i, and i 2 3

Important (really) i 0 = 1 i 1 = i i 2 = –1 i 3 = –i i 4 = : Defining Complex Numbers, i, and i 2 4

Practice Rewrite the radical using the imaginary unit i : Defining Complex Numbers, i, and i 2 5

Solution Rewrite the value under the radical as the product of –1 and a positive value. Rewrite the radical as i : Defining Complex Numbers, i, and i 2 6

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 : Defining Complex Numbers, i, and i 2 7

Can you… Simplify i : Defining Complex Numbers, i, and i 2 8

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