Area bounded by - 8 z 2 - 8 z ¯ ? 2 + 20 z z ¯ = 144 is (where z is a complex number):

Question

Area bounded by $- 8 z^{2} - 8 {\bar{z}}^{2} + 20 z \bar{z} = 144$ is (where $z$ is a complex number):

Smart Achievers · Accepted Answer

(3)

$Let z = x + i y$

$- 8 ({(x + i y)}^{2} + {(x - i y)}^{2}) + 20 (x^{2} + y^{2}) = 144$

$- 8 (2 (x^{2} - y^{2})) + 20 (x^{2} + y^{2}) = 144$

$4 x^{2} + 36 y^{2} = 144$

$\frac{x^{2}}{36} + \frac{y^{2}}{4} = 1$

$a = 6, b = 2$

$Area = π a b = 12 π$

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