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EternalSummer247

USA
Joined: Jul 6, 2007
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Rewriting an Expression in the form a+bi

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I have this problem:

If we rewrite the expression

1/1-i - 1/i

in the form a+bi (i^2=-1), the result will be...

The furthest I have gotten in solving this is

1/2-1/i

But the book says the answer is:

1/2+3/2i

I'm brand new to this, so what am I doing wrong?

[Dec 2, 2008 3:37:29 PM]

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pskinner

Joined: Apr 2, 2005
Posts: 694
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Re: Rewriting an Expression in the form a+bi

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The technique is to "rationalize the denominator" by multiplying by the conjugate:

1/(1-i)=1*(1+i)/[(1-i)(1+i)]=(1+i)/[1-i^2]=(1+i)/[1+1)=(1/2)(1+i)=1/2+(1/2)i

As for the second fraction:

-1/i=-1*i/(i*i)=-i/[i^2]=-i/(-1)=i

Now, you can add the two fractions to get the book answer.
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Principal Skinner

[Dec 3, 2008 10:04:05 AM]

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