My Math Forum putting in form z=x+iy

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February 27th, 2017, 05:24 AM   #1
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putting in form z=x+iy

Please could some one help with how to put this equation into the form x+iy=z as I am stuck
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 February 27th, 2017, 06:04 AM #2 Senior Member     Joined: Sep 2015 From: CA Posts: 908 Thanks: 489 $z^2 + 2z - i \sqrt{3} = 0$ complete the square $(z+1)^2 - 1 - i\sqrt{3} = 0$ $(z+1)^2 = 1+i\sqrt{3}$ $z+1 = \pm \sqrt{1+i\sqrt{3}}$ $z = -1 \pm \sqrt{1+i\sqrt{3}}$ Now we need to deal with the radical. $1+i\sqrt{3} = 2e^{i\pi/3}$ $\sqrt{1+i\sqrt{3}} = \sqrt{2}e^{i\pi/6} = \sqrt{\dfrac 3 2 }+\dfrac{i}{\sqrt{2}}$ so $z = -1 + \sqrt{\dfrac 3 2 }+\dfrac{i}{\sqrt{2}}$ $z = -1 - \sqrt{\dfrac 3 2 }-\dfrac{i}{\sqrt{2}}$ Thanks from Andrzejku98

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