# Math Help - Solve for a and b if:

1. ## Solve for a and b if:

Solve for a and b if: (jb)/(1-j)=(a-j)2j

Any help will be much appreciated.

2. ## Re: Solve for a and b if:

Originally Posted by Scoplex
Solve for a and b if: (jb)/(1-j)=(a-j)2j

Any help will be much appreciated.
$\frac {b\cdot j}{1-j}=2+2a \cdot j \Rightarrow b \cdot j =(2+2a \cdot j)(1-j) \Rightarrow$

$\Rightarrow b \cdot j = (2a+2) +(2a-2) \cdot j \Rightarrow$

$\Rightarrow 2a-2 = b ~\text {and}~2a+2=0$

3. ## Re: Solve for a and b if:

Originally Posted by princeps
$\frac {b\cdot j}{1-j}=2+2a \cdot j$
How did you arrive at 2 + 2aj?
Isn't it 2aj - 2j^2 ?

4. ## Re: Solve for a and b if:

Originally Posted by Wilmer
How did you arrive at 2 + 2aj?
Isn't it 2aj - 2j^2 ?
$j^2=-1$

5. ## Re: Solve for a and b if:

(j*b) / (1 - j) = 2*j*(a - j)

We're to solve for a and b;
b is straightforward: b = [2j(a - j)(1 - j)] / j

a = [2j(j - 1) - b] / [2(j -1)]

That checks out perfectly with the initial equation.
And there's loads of solutions; examples with all positive integers:
(a,b,j) = (1,2,2), (2,4,3), (1,8,3), (3,6,4), (4,8,5)

I think that $j$ is imaginary unit .
I think that $j$ is imaginary unit .