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Complex Number Problem

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Let z be a complex number satisfying 2z + 3*(Conjugate Z) = - 25 - 2i. What is the value of z?
Any help would be nice, It would also be helpful if there was an explanation, thanks. I would really like to learn how to do this.

Oct 12, 2018
edited by Guest  Oct 12, 2018
edited by somebody  Oct 12, 2018

#1
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$$2z+3z^* = -25 - 2i \\ \text{let }z=x+i y \\ 2(x+i y) + 3(x - i y) = 25 -2i \\ 5x - i y = 25-2i\\ x=5, y=2 \\ z = 5 + 2i \\$$

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Oct 12, 2018
#2
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Hi Rom, this was my initial answer, but it is apparently wrong.

somebody  Oct 12, 2018
#3
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$$\text{Oh, my bad it's }-25 - 2i \\ 2(x+i y) + 3 (x - i y ) = -25 - 2i \\ 5x - i y = -25 - 2i \\ x = -5, ~y=2 \\ z= -5 +2 i$$

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Oct 12, 2018