In this Grade 8 Algebra 2 lesson from Big Ideas Math Chapter 3, students learn to define and use the imaginary unit i, write complex numbers in standard form a + bi, and identify the subsets of complex numbers including real, imaginary, and pure imaginary numbers. Students practice finding square roots of negative numbers, adding, subtracting, and multiplying complex numbers, and finding complex solutions to quadratic equations. The lesson builds a foundational understanding of how the complex number system extends the real number line to include imaginary numbers.
Section 1
Square Root of a Negative Number
The imaginary unit is the number whose square is .
Square Root of a Negative Number
If is a positive real number, then
Complex Number
A complex number is of the form , where and are real numbers.
Section 2
Equality of Complex Numbers
Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal:
Section 3
Add and Subtract Complex Numbers
Adding and subtracting complex numbers is much like adding or subtracting like terms. We add or subtract the real parts and then add or subtract the imaginary parts. Our final result should be in standard form, .
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Section 1
Square Root of a Negative Number
The imaginary unit is the number whose square is .
Square Root of a Negative Number
If is a positive real number, then
Complex Number
A complex number is of the form , where and are real numbers.
Section 2
Equality of Complex Numbers
Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal:
Section 3
Add and Subtract Complex Numbers
Adding and subtracting complex numbers is much like adding or subtracting like terms. We add or subtract the real parts and then add or subtract the imaginary parts. Our final result should be in standard form, .
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter