## 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?

# Multiplying Complex Numbers, Day 1 of 4

Unit 2: The Complex Number System
Lesson 8 of 16

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

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Standards:
Subject(s):
Math, Algebra, Algebra 2, master teacher project, complex numbers, Imaginary Numbers
45 minutes

### Jacob Nazeck

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