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Math 96
Chapter 10.7 (Complex Numbers)
6
Mathematics
Undergraduate 3
03/12/2012

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Cards

Term
The imaginary unit i
Definition
  • √-1 = i  You cannot square a negative number.
  • √-100 = i√100 = 10i
  • -√-16 = -i√16 = -4i
  • √-96 = i√96 = 4i√6

 

Term
The power of i
Definition
  • i = i
  • i2 = -1
  • i3 = -i    because i + i2 = i + -1 = -i
  • i4 = 1  because i2 + i2 = -1 + -1 = 1
  • etc...
Term
Multiply complex number
Definition
  • √-11 . √-3 =  i√11 . i√3 = i2 √33 = -1√33
  • √-49 . √-100 = i√49 . i√100 = 7i . 10i = 70i2 = -70
Term
Dividing complex numbers
Definition
√-28 ⁄ √7 = i√28 ⁄ √7 = 2i√7 ⁄  √7 = 2i
Term
Add imaginary unit
Definition

(6 - i) + (-7 + 6i)

= 6-7 + -i + 6i

= -1 + 5i

Term
Write the quotient in the form of a + bi
Definition
  • Multiply the denominator on both nominator and denominator but change the sign. example: 2/1-i = 2/1-i . 1+i/1+i  and distribute.
  • When multiplying 2 binomials FOIL

 

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