Question

Multiply the following complex numbers.

1/1+i times 1-i/1-i
Reduce terms and simplify. Explain how your simplified result and the first term in the pair below are related algebraically to each other and to the complex number (1 + i).

Answer 1

Multiplying the complex numbers we get:
(1+i)×(1-i/1-i)
=1(1-i/1-i)+i(1-i/1-i)
=(1×1)+(-i/1×1)+(1×-i)+(i×1)+(i×-i/1)+(-i×i)
=1-i/1-i+i+1+1
=1-i-i+i+1+1
=3-i
The relation between our answer and 3-i, is that they (1+i) is that they have been made by real parts and complex parts.