.
Multiplication
   Problem 1.1 (complexity 1). Solution

If   and   , find z1 · z2 = x+iy.
Solution 1

By the definition,
z1·z2  
   
   
Solution 2

By formally manipulating the terms as if they involved only real numbers and by replacing i2 by -1 when it occurs,
z1·z2  
   
   
   
   
   


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