# Math help

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#### shermaine

##### New Member
Hi,

How do i calculate this?

50[(1 + 0.91 + j3.14) / (1 - 0.91 - j3.14)] = -49.1 + j31.8?

#### JimB

##### Super Moderator
First, simplify top and bottom to give:

50 x (1.91 + j3.14) / (0.09 - j3.14)

Now multiply top and bottom by (0.09 + j3.14), this will get rid of the j term on the bottom.
Just keep thrashing out the numbers and it works out fine.

JimB

#### EN0

##### Member
Hello,

j is just a variable in this case, correct?

Last edited:

#### JimB

##### Super Moderator
j is just a variable in this case, correct?
No, quite wrong actually.

JimB

#### shermaine

##### New Member
how do i get j31.8?

#### Papabravo

##### Well-Known Member
You learn the rules of complex algebra, and pay very careful attention to signs as you expand the binnomials.

What JimB told you was to convert the compex number in the demoninator to a real number, by multiplying it by it's complex conjugate. The complex conjugate of a number is just the original complex number with the sign of the imaginary part inverted.

Code:
In our example:
if d = 0.09 - 3.14j then d*, the complex conjugate of d, is
d* = 0.09 + 3.14j
and
dd* = (0.09 - 3.14j)*(0.09 + 3.14j)
= 0.0081  + 0.2826j - 0.2826j - 9.8596j²
= 0.0081 + 9.8596
= 9.8677

That is the denominator -- it's a real number, no imaginary part.
Now in order to keep everything the same we need to multiply the numerator
by the complex conjugate of the denominator.  If we started with n/d
and multiply both top and bottom by the complex conjugate of d we
have nd*/dd*, and clearly d*/d* = 1

50*(1.91 + 3.14j)*(0.09 + 3.14j)
= 50*(0.1719 + 5.9974j + 0.2826j + 9.8596j²)
= 50*(-9.6867 + 6.28j)
So the final result should be
50*(-9.6877 + 6.28j) / 9.8677
= -49.0879 + 31.821j
which rounds nicely to 3 significant figures as -- ta da
= -49.1 + 31.8j
It also helps if you have a kick-ass calculator, like a TI-92, that will do the problem for you; but that is for after you graduate and go on to make big bucks in industry.

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#### Roff

##### Well-Known Member
Hello,

j is just a variable in this case, correct?
j is the imaginary operator, also represented by i.
j=√(-1).

#### RCinFLA

##### Well-Known Member
You may find it easier to work with polar number (phasor) representation of complex numbers. 1.91 + j3.14 = 3.675 at angle of +58.689 degrees.

Dividing and multiplying polar number is very easy.

Adding and subtracting complex numbers is very easy.

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#### Papabravo

##### Well-Known Member
You still have to watch the signs as you crunch the numbers.

#### shermaine

##### New Member
Guys, thanks so much for the help.
I understand it now. I keep using polar, complex to do. No wonder i cant get the answers. Thanks.

#### EN0

##### Member
j is the imaginary operator, also represented by i.
j=√(-1).

Thanks, Ron! I'll do that!

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