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Solve the equation $z+2z^*=\frac{15}{2+i}$.

I want to ask what's the meaning of $z^*$?

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I think it means $\bar z$ the complex conjugate of z

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  • $\begingroup$ What is $z$ here? $\endgroup$ – Mathxx Oct 18 '15 at 17:18
  • $\begingroup$ You are asked to find it, it's like solving and equation for x, but now z is a complex number ie $z = a + ib$ so $z^* = a - ib$ $\endgroup$ – Noctisdark Oct 18 '15 at 17:20
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    $\begingroup$ ;), if you don't need anymore assistant you can mark this answered ! $\endgroup$ – Noctisdark Oct 18 '15 at 17:22
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Write $z=x+iy$ then $z^•=x-iy$ and $z+2z^*=3x-iy$ and our equation looks like

$$3x-iy={15\over 5}(2-i)=6-3i$$

and so $z=2+3i$

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  • $\begingroup$ Um, $z+z^*=2x$, not $2x-iy$. The $iy$s cancel. $\endgroup$ – Akiva Weinberger Oct 18 '15 at 17:45
  • $\begingroup$ I edit thanks @Akiva Weinberger $\endgroup$ – marwalix Oct 18 '15 at 18:33
  • $\begingroup$ Then $z+2z^*=(x+iy)+(2x-2iy)=3x-iy$. $\endgroup$ – Akiva Weinberger Oct 18 '15 at 23:41

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