- #1
glauss
- 13
- 1
- Homework Statement
- Find c and d when:
a, b E R and a, b !=0
1/(a+bi)=c+di
Additionally, prove that (a+bi) has a multiplicative inverse.
- Relevant Equations
- 1/(a+bi)=c+di
I have as a solution for part one:
c=(a)/(a^2 + b^2)
d=(-b)/(a^2 + b^2)
Which matches with the solution manual.
The manual goes on to give the solution for part b:
(a+bi) * ( (a)/(a^2 + b^2) - ((b)/(a^2 + b^2))i ) = 1
I'd simply like to know where the 'i' at the end of the second expression in the left part comes from.
c=(a)/(a^2 + b^2)
d=(-b)/(a^2 + b^2)
Which matches with the solution manual.
The manual goes on to give the solution for part b:
(a+bi) * ( (a)/(a^2 + b^2) - ((b)/(a^2 + b^2))i ) = 1
I'd simply like to know where the 'i' at the end of the second expression in the left part comes from.