Complex number question

[cosmic]

Hi guys,

I'm asked to write the fraction (-6+i)/(-5+6i) as a single simplified complex number in the form of a+bi.

I calculated the answer as 1/61(24+31i)

I would really appreciate if someone could check to see whether it's correct or not.

Thanks in advance.

 

[stapel]

I'm asked to write the fraction (-6+i)/(-5+6i) as a single simplified complex number in the form of a+bi.

I calculated the answer as 1/61(24+31i)

Since this is not of the required form, I'm not sure how you're expecting this to be the expected answer...?

Also, aren't you supposed to rationalize denominators? Surely the 24 + 31i shouldn't be in the denominator with the 6...?

 

[cosmic]

Since this is not of the required form, I'm not sure how you're expecting this to be the expected answer...?

Also, aren't you supposed to rationalize denominators? Surely the 24 + 31i shouldn't be in the denominator with the 6...?

Thanks for replying.

1/61(24+31i) is equivalent to 24/61+31i/61 which is of the form a+bi. Sorry I wasn't being clear.

Also to divide complex numbers don't you just multiply the numerator and the denominator by the complex conjugate of the denominator?

 

[cosmic]

I just realised that I made a mistake with one of the signs.

The answer I get now is 36/61+31i/61

Is that any good?

 

[cosmic]

Correct.
You can check yourself; substitute i = sqrt(-1) in original expression,
then in your expression: both should come out same...OK?

Thanks Denis. Much appreciated.

 

[pka]

I'm asked to write the fraction (-6+i)/(-5+6i) as a single simplified complex number in the form of a+bi.

Learn this identity: \(\displaystyle \displaystyle\frac{1}{z} = \frac{{\overline z }}{{{{\left| z \right|}^2}}}\).

Using it: \(\displaystyle \displaystyle\frac{1}{{ - 5 + 6i}} = \frac{{ - 5 - 6i}}{{25 + 36}}\) so that \(\displaystyle \displaystyle\frac{{ - 6 + i}}{{ - 5 + 6i}} = \frac{{\left( { - 6 + i} \right)\left( { - 5 - 6i} \right)}}{{61}}\)

 

[cosmic]

Learn this identity: \(\displaystyle \displaystyle\frac{1}{z} = \frac{{\overline z }}{{{{\left| z \right|}^2}}}\).

Using it: \(\displaystyle \displaystyle\frac{1}{{ - 5 + 6i}} = \frac{{ - 5 - 6i}}{{25 + 36}}\) so that \(\displaystyle \displaystyle\frac{{ - 6 + i}}{{ - 5 + 6i}} = \frac{{\left( { - 6 + i} \right)\left( { - 5 - 6i} \right)}}{{61}}\)

Thanks Pka that's really useful. The identity I used is similar but I managed to mix the signs up initially.

 

[lookagain]

I just realised that I made a mistake with one of the signs.

The answer I get now is 36/61+31i/61 <------- You don't have the "b" separate and to the left of "i" in the a + bi form.

Is that any good?

It's almost there.

In horizontal form, this would count:

36/61 + (31/61)i


Or, you could have this in a vertical form:

\(\displaystyle \dfrac{36}{61} + \dfrac{31}{61}i\)

 

[Ishuda]

Hi guys,

I'm asked to write the fraction (-6+i)/(-5+6i) as a single simplified complex number in the form of a+bi.

I calculated the answer as 1/61(24+31i)

I would really appreciate if someone could check to see whether it's correct or not.

Thanks in advance.

Assuming you meant
(1/61)(24+31i)
then you should re-write it with a=24/61 and b=31/64. As far as being correct otherwise, I believe you may have incorrectly multiplied -6i and i

Well spit - maybe I should read every thing there before I say what has been said before. oh well, I'll blame it on my blindness right