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Reduce complex number expressions

CONCEPTS

Real vs imaginary numbers

• Real #: root of a positive number (ex: ³√x)

• Imaginary number: root of a negative number (ex: ³√(–x)). An imaginary number is notated with the letter i after the number (Ex: 5i, 2i, -3i, i). Values of imaginary numbers include i = √-1, i² = -1, i³ = - √-1, i⁴ = 1

• Complex number: includes a real and imaginary number. It is in the form a + bi where a is the real number and bi is the imaginary number


Tips

• Group all real terms together & all imaginary terms together

PRACTICE PROBLEMS

Question 1 For a complex number i and an integer x, what is a possible value of iˣ?

Options: 0, 1, 2, 3, 4


-- Answer -- 4

i = √-1

i² = -1

(i²)² = 1, i⁴ = 1

ACT PRACTICE PROBLEMS

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