Complex Numbers

Basics of Complex Numbers

Types of Problems:

  • What is "i"?
  • What is "a+bi"?
  • Be able to to plot a complex number on the complex number plane
  • Be able to completely simplify expressions that involve i
  • Be able to rewrite any power of i as -1, 1, i, or -i
  • Determine the absolute value of a complex number
  • What is a complex conjugate?

Notes & Handouts

Practice 

Video and other resources

Digital Resources

Addition and Subtraction of Complex Numbers

Types of Problems:

  • Be able to add and subtract complex numbers properly and write the resulting sum or difference as a completely simplified complex number

Notes & Handouts

Practice

​Video and other resources

​Digital Resources

Multiplication of Complex Numbers

​Types of Problems:

  • Be able to multiply complex numbers properly and write the resulting product as a completely simplified complex number

​Practice

​Video and other resources

​Notes & Handouts

Division of Complex Numbers

​Types of Problems:

  • Be able to divide complex numbers properly and write the resulting quotient as a completely simplified complex number
  • Be able to use a complex conjugate to simplify rational expression that involves complex numbers 

​Practice

​Video and other resources

​Notes & Handouts

​Digital Resources

Raising a Complex Number to a Power

​​Types of Problems:

  • Be able to expand powers of complex numbers properly and write the result as a completely simplified complex number
  • Understand how to use the remainder of a quotient to simplify powers of i
  • Properly apply algebraic expansion to expressions involving complex numbers  

​​Notes & Handouts

​​Practice

​Video and other resources

​Digital Resources

Complex Numbers in Trigonometric Form

​​Types of Problems:

  • What is the equivalent form of a complex number in trigonometric form?
  • How do you convert a+bi into "r" and "theta"?
  • Determine the modulus of a complex number
  • Determine the argument of a complex number

​​Practice

​Video and other resources

​​Notes & Handouts

​Digital Resources

Advanced Operations and Concepts related to Complex Numbers

​​Types of Problems:

  • DeMoivre's Theorem
  • nth roots of a Complex Number
  • nth roots of a Real Number
  • Euler's Formula

​​Practice

​​Video and other resources

​​Notes & Handouts

Digital Resources