Reflection: Real World Applications Multiplying Complex Numbers, Day 1 of 4 - Section 3: Multiplication of Complex Numbers


When teaching complex numbers, I often get the question, "What's the point of all this?"  It's hard enough to understand why mathematicians would want to say that the square root of -1 is a number, but it's even harder to imagine how this fiction could be useful

However, they are all familiar with vectors from their science classes, so I'll point out to them that complex numbers are vectors.  Since scientists often need to work with vectors, complex numbers can be helpful.  Also, since every complex number contains 2-dimensional information, they can be used in many cases where two separate numbers would be inconvenient.  This is why complex numbers are used in the study of wave motion; a single number can contain information about both amplitude and phase shift.  Finally, it's worth noting that the definition of distance (modulus) and argument amount to a translation from rectangular to polar coordinates.  For many students, this is their first exposure to such a notion.

  What's the point?
  Real World Applications: What's the point?
Loading resource...

Multiplying Complex Numbers, Day 1 of 4

Unit 2: The Complex Number System
Lesson 8 of 16

Objective: SWBAT use the unit imaginary number and the field axioms to multiply complex numbers. SWBAT represent and interpret multiplication of complex numbers in the complex number plane.

Big Idea: Students explore and explain correspondences between numerical and graphical representations of arithmetic with complex numbers.

  Print Lesson
2 teachers like this lesson
Math, Algebra, Algebra 2, master teacher project, complex numbers, Imaginary Numbers
  45 minutes
complex number mod and arg
Similar Lessons
Review of Complex Numbers
12th Grade Math » Vectors and Complex Numbers
Big Idea: How is a complex number in standard form similar to a vector in unit vector form?
Independence, MO
Environment: Suburban
Katharine Sparks
Radical HAMGO
Algebra II » Let's Explore Radicals!
Big Idea: HAMGO - BINGO! Turn your lesson into a fun game with lots of skills practice!
Huntington, IN
Environment: Suburban
Jarod Hammel
The Real Number System
Algebra II » Complex Numbers and Quadratic Equations
Big Idea: This lesson relates the real number system to its historical perspective.
Caldwell, ID
Environment: Rural
Amelia Jamison
Something went wrong. See details for more info
Nothing to upload