Solutions: Working with Complex Numbers

Evaluate the following:
  1. (3-4i) + (-6+2i)

    Collect "like terms":

    (3-4i)+(-6+2i)=3-4i-6+2i=(3-6)+(-4i+2i)=-3-2i

  2. (3-4i)(-6+2i)

    Use FOIL (First-Outer-Inner-Last, which is really just the distributive property):

    (3-4i)(-6+2i)=(3)(-6)+(3)(2i)+(-4i)(-6)+(-4i)(2i)=-18+6i+24i-8i2

    To finish it off, use that i2=-1:

    (3-4i)(-6+2i)=-18+6i+24i-8(-1)=(-18+8)+(6i+24i)=-10+30i

  3. (1+i)2

    Use FOIL again, and wherever you see i2, replace it with -1:

    (1+i)2=(1+i)(1+i)=1+i+i+i2=1+2i+(-1)=2i


Figures describing the Mandelbrot process, from textbook

Back to Fractals | Back to Inclass