12th Grade Complex Numbers Lesson Plan Example (Math)

Topic: complex numbers

Objectives & Outcomes:

• Understand the definition and properties of complex numbers.
• Be able to use complex numbers in geometric applications, including polar coordinates and Cartesian coordinates.

Materials

• Complex numbers chart
• Complex number worksheets
• Polar coordinate graph paper
• Pencils
• Calculator (optional)

Warm-up

• Ask students if they have heard of complex numbers before. Allow a few students to share their knowledge of complex numbers and their applications.
• Discuss the applications of complex numbers in geometric modeling and in solving equations.

Direct Instruction

• Introduce the concept of a complex number as a combination of a real number and a imaginary number.
• Explain the notation for complex numbers, including the use of the symbol "i" to denote the imaginary part and the use of the symbol "j" to denote the conjugate of a complex number.
• Demonstrate how to add and subtract complex numbers using the complex number notations.
• Explain how to multiply and divide complex numbers using the complex number notations.
• Introduce the concept of the geometrical representation of complex numbers using the rectangular coordinate system.
• Demonstrate how to solve equations involving complex numbers using the geometrical representation.

Guided Practice

• Provide the students with a few complex numbers and ask them to add, subtract, multiply and divide the numbers using the complex number notations.
• Have the students work in pairs to solve a set of complex number equations using the geometrical representation.

Independent Practice

• Provide the students with a set of complex number equations and ask them to solve the equations using the geometrical representation.
• Have the students choose a real number a and a complex number b = a + i·θ, where θ is a real number. Then, have them find the complex number a - b using the geometrical representation and explain the meaning of the result.

Closure

• Ask the students to share their work with the class and explain the geometrical representation and the meaning of the complex number a - b.
• Summarize the lesson by highlighting the key points and concepts covered.

Assessment

• Collect the students' work and assess their understanding of complex numbers and their ability to represent and interpret complex numbers geometrically.