(a+bi)i=1, what is the value of a and b?

Question

A complex number a+bi can be multiplied by i to get 1.  What is value of a-b? (Note: i²=-1.)

Answer 1

(a + bi)i = 1

 

ai + bi² = 1

 

ai - b = 1

 

-b + ai = 1 + (0)i

 

-b = 1 

a = 0

 

b = -1

a = 0