The solutions to the complex numbers practice problems are:

1. (3 + 2i) + (4 - i) = 3 + 4 + 2i + -i = 7 + i

2. (-3.5 + 0.2i) + (1 + .45i) = -3.5 + 1 + .2i + .45i = -2.5 + .65i

3. (.83 + .4i) + (.25 - .32i) = .83 + .25 + .4i + -.32i = 1.08 + .08i

Notes on multiplication:

• You do not have to do it exactly the same way I do, so long as you are doing it a way that makes sense and always leads to the correct answer. 
  
• You do not have to show as much work as I do, but you do have to show some work between the problem and the answer.
  
• If your problem has decimals in it, you do not have to show all of the decimal places, but you do need to show at least 2 decimal places, and you do need to round correctly.
  

4. (3 + 2i)(4 - i) = 3*4 + 3*(-i) + 2i*4 + 2i*(-i) = 12 + -3i + 8i + -2i² = 12 + 5i + 2 = 14 + 5i

5. (-3.5 + 0.2i)(1 + .45i) = -3.5*1 + -3.5*.45i + .2i*1 + .2i*.45i  = -3.5 + -1.575i + .2i +  .09i² = -3.5 + -1.375i + -.09 = -3.59 - 1.375i

6. (.83 + .4i)(.25 - .32i) = .83*.25 + .83*(-.32i) + .4i*.25 + .4i*(-.32i) = .2075 + -.2656i + .1i + -.128i²  = .2075  - .1656i + .128 =  .3355 - .1656i

7. Plot each of these on a complex plane, and label them:

A. 3 + 2i B. -3.5 + 0.2i C. 0.25 - .32i