Exercise 7.  Prove that the complex number     (which we identify with the real number 1)  is the multiplicative identity for complex numbers.

Solution 7.

See text and/or instructor's solution manual.

Use the (ordered pair) definition for multiplication to verify that if    is any complex number, then  .  

Use the multiplication rule  .

Multiply on the left and get:   .  

Multiply on the right and get:   .  

Therefore,   is the the multiplicative identity for complex numbers.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell