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Plotting Sums and Differences of Complex Numbers

Sum: (a+bi)+(c+di)-(a+c)+(b+d)i

   Real         Imaginary

Difference: (a+bi)-(c+di)=(a-c)+(b-d)i

Examples:

a. (4-i)+(3+2i)
b. (7-5i)-(1-5i)
c. 6-(-2+9i)+(-8+4i)

a. (4-i)+(3+2i)=(4+3)+(-1+2)i=7+1i=\fbox{7+i}

a=4,\ c=3
b=-1,\ d=2

b. (7-5i)-(1-5i)=(7-1)+(-5-(-5))i=6+(-5+5)i=6+(0)i=\fbox{6}

c. 6-(-2+9i)+(-8+4i)=(6+0i)-(-2+9i)+(-8+4i)

    1. Difference:
      [(6-(-2))+(0-9)i]+(-8+4i)
      =[(6+2)+(-9)i]+(-8+4i)
      =(8-9i)+(-8+4i)
    2. Sum:
      =[(8+-8)+(-9+4)i]
      =0+(-5i)
      \fbox{-5i}