- #1
TheDoorsOfMe
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Homework Statement
Suppose a and b are real numbers, not both 0. Find real numbers c and d, such that
[tex]\frac{1}{a + bi}[/tex] = [tex]c + di[/tex]
Homework Equations
I said that:
[tex] 1 = (c + di) (a + bi) [/tex]
[tex] 1 = (ac - bd) + (bc + ad)i [/tex]
so if b = 0 then
[tex]\frac{1}{a} = c + di[/tex]
The rationale holds for if a = 0. Since this is equal to a real number 1/a can I just say that c and d are real numbers?