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I can't solve this set of equations, please help me.

$(1+i)z_1 + (1-i)z_2 = 1+i$ $(1-i)z_1 + (1+i)z_2 = 1+3i$

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    Please show what you have done. It's exactly the same process as you would solve a system of equations with real numbers, except that you are computing with complex numbers instead of real numbers.2011-10-23

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One way is to multiply the top equation through by $(1-i)$ and the bottom one by $(1+i)$ to give

$2z_1 - 2iz_2 = 2\qquad\qquad$ $2z_1 + 2iz_2 = -2+4i$

You can now eliminate one of the unknowns and find the other. You can then substitute this back and get the complete solution.

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    Added the two equations together. More formally $2iz_2=2z_1-2$ and $2iz_2 = -2 +4i -2z_1$2011-10-24
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Hints: Gaussian Elimination and Cramer's Rule.

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    @Ruslan Slavenok. It is the way you used to solve two linear equations in two unknowns in early algebra. The only difference is that the numbers are non-real. You can also add the two equations, divide by $2$ to get an equation $z_1+z_2=$ and subtract the second equation from the first, divide by $2i$, to get $z_1-z_2=$. Then I think it will look very familiar. But the first way I described is more general.2011-10-23