Xm yn - 1xm yn - 2 cos m- - n-

x^my^n #160; = #160; (e^iθ)^m #160; (e^iϕ #160; )^n #160; = #160; e^imθ #160; #160; + #160; nϕ∴ #160; 1x^my^n #16 ...

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Sign of Trigonometric Ratios in Different Quadrants

xm yn + 1xm...

Question

$x^{m} y^{n} + \frac{1}{x^{m} y^{n}} = 2 c o s (m θ + n ϕ)$

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Solution

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x = c o s θ + i s i n θ a n d y = c o s ϕ + i s i n ϕ, t h e n x^{m} y^{n} + x^{- m} y^{- n}

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