(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant 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?

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# Homework Help: Complex number question

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