SOLUTION: find two imaginary numbers in the form a + bi whose product = 17. Neither a nor b may equal zero. Has me stumped. Any help is appreciated.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: find two imaginary numbers in the form a + bi whose product = 17. Neither a nor b may equal zero. Has me stumped. Any help is appreciated.      Log On


   

Question 136433: find two imaginary numbers in the form a + bi whose product = 17. Neither a nor b may equal zero.
Has me stumped. Any help is appreciated.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In order to get rid of any i in the result, the factors
would have to be of the form a+%2B+bi and a+-+bi, then
%28a+%2B+bi%29%28a+-+bi%29+=+a%5E2+-+b%5E2%2A%28-1%29
a%5E2+-+b%5E2%2A%28-1%29+=+a%5E2+%2B+b%5E2, and it's given that
a%5E2+%2B+b%5E2+=+17
I know that 16 and 1 are both squares and add up to 17, so
4%5E2+%2B+1%5E2+=+17
a+=+4
b+=+1
So, the numbers are
4+%2B+i and
4+-+i