Complex Numbers

As_Dust_Dances_

For this question, I'm just wondering whether there is a much simpler way to solve for x and y rather than treating the 2 fractions separately and multiplying by the complex conjugates for each.

Original post by As_Dust_Dances_

For this question, I'm just wondering whether there is a much simpler way to solve for x and y rather than treating the 2 fractions separately and multiplying by the complex conjugates for each.

In this case, yes there is.

Move the 1/(1+2i) to the RHS via subtraction.

Put the RHS over a common denominator and simplify.

Invert both fractions and simplify the RHS.

First write

\frac 1 {x+iy} = \frac{2i}{1 + 2i}

Then multiply the top and bottom of the RHS by

\frac 1{2i}

...might save a little time.

As_Dust_Dances_

OP

Original post by jb444

First write

\frac 1 {x+iy} = \frac{2i}{1 + 2i}

Then multiply the top and bottom of the RHS by

\frac 1{2i}

...might save a little time.

Unfortunately I don't have the answer at hand, but I'm getting x = 1 and y = -1/2 (is this correct from your calculations?)

Original post by As_Dust_Dances_

Unfortunately I don't have the answer at hand, but I'm getting x = 1 and y = -1/2 (is this correct from your calculations?)

Yes.

As_Dust_Dances_

OP

Original post by ghostwalker

Yes.

Thanks for your help :smile:

:smile:

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