Section 1.4 - Complex Numbers

Section 1.4 - Complex Numbers

1. The Imaginary Unit i

   • i = square root less than equal to -1
   • where i^2 = -1

2. A set of complex numbers

   • a+bi
     • a = real number
     • b = imaginary number
     • b not equal to 0
     • bi = pure imaginary number

3. Equity of Complex Numbers

   • a+bi = c+di if a=c and b=d

4. Adding and Subtracting Complex Numbers

   • Adding (a+bi) + (c+di) = (a+c) + (b+d)i
   • Subtracting (a+bi) - (c+di) = (a-c) + (b-d)i

5. Conjugate of a Complex Number

   • a+bi = a-bi
     • (a+bi)(a-bi) = a^2 + b^2
   • a-bi = a+bi
     • (a-bi)(a+bi) = a^2 + b^2

6. Principle Square Root of a Negative Number

   • square root -b = i square root b