In this Grade 11 enVision Algebra 2 lesson, students learn to define and work with complex numbers in the form a + bi, including the imaginary unit i and its property i² = −1. The lesson covers adding, subtracting, and multiplying complex numbers, as well as identifying complex conjugates and simplifying quotients with imaginary denominators. Students also solve quadratic equations with no real solutions, such as x² = −9, by expressing results using 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
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, .
Expand to review the lesson summary and core properties.
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
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, .