The figure in the complex plane given by 10 z | vedclass

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(A) Let $z = x + iy$,then $\bar{z} = x - iy$.We have $z \bar{z} = x^2 + y^2$,$z^2 = x^2 - y^2 + 2ixy$,and $\bar{z}^2 = x^2 - y^2 - 2ixy$.Substituting

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a straight line

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(A) Let $z = x + iy$,then $\bar{z} = x - iy$.We have $z \bar{z} = x^2 + y^2$,$z^2 = x^2 - y^2 + 2ixy$,and $\bar{z}^2 = x^2 - y^2 - 2ixy$.Substituting these into the equation $10 z \bar{z} - 3(z^2 + \bar{z}^2) + 4i(z^2 - \bar{z}^2) = 0$:$10(x^2 + y^2) - 3(2(x^2 - y^2)) + 4i(4ixy) = 0$$10(x^2 + y^2) - 6(x^2 - y^2) - 16xy = 0$$10x^2 + 10y^2 - 6x^2 + 6y^2 - 16xy = 0$$4x^2 - 16xy + 16y^2 = 0$Dividing by $4$,we get $x^2 - 4xy + 4y^2 = 0$,which is $(x - 2y)^2 = 0$.This represents the straight line $x - 2y = 0$.

The figure in the complex plane given by $10 z \bar{z} - 3(z^2 + \bar{z}^2) + 4i(z^2 - \bar{z}^2) = 0$ is

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