FP1 Complex Numbers - Help please! Watch

duckd0nald
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I'm struggling with this question, can someone please help?

\[z=\frac{a+2i}{a-i}\]
Given that the real part of z is \frac{1}{2}, what is the value of a?

I tried to realise the denominator, but that just gave me quadratics. I also tried to multiply \frac{1}{2}\+bi by a-i, but that was inconclusive.
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Mr M
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(Original post by duckd0nald)
I'm struggling with this question, can someone please help?

\[z=\frac{a+2i}{a-i}\]
Given that the real part of z is \frac{1}{2}, what is the value of a?

I tried to realise the denominator, but that just gave me quadratics. I also tried to multiply \frac{1}{2}\+bi by a-i, but that was inconclusive.
Multiply by \frac{a+i}{a+i} and then consider the real part.
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duckd0nald
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(Original post by Mr M)
Multiply by \frac{a+i}{a+i}
\frac{a^2+3ai-2}{a^2+1}=\frac{1}{2}+qi
I don't understand what I do after that.
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Mr M
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(Original post by duckd0nald)
\frac{a^2+3ai-2}{a^2+1}=\frac{1}{2}+qi
I don't understand what I do after that.
Just look at the real part.
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duckd0nald
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(Original post by Mr M)
Just look at the real part.
\frac{1}{2} = \frac{a^2-2}{a^2+1}
Like so?
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Mr M
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(Original post by duckd0nald)
\frac{1}{2} = \frac{a^2-2}{a^2+1}
Like so?
Yes. Presumably you can solve that equation?
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duckd0nald
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(Original post by Mr M)
Yes. Presumably you can solve that equation?
Ah, right. Thank you!
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