<p>a) Where is the function <img title=\"f(z) = e^{{x^2} - {y^2}}[\\cos(2xy) + i

Question

<p>a) Where is the function <img title="f(z) = e^{{x^2} - {y^2}}[cos(2xy) + i sin(2xy)] " src="https://latex.codecogs.com/png.latex?f%28z%29%20=%20e%5E%7B%7Bx%5E2%7D%20-%20%7By%5E2%7D%7D[%5Ccos%282xy%29%20+%20i%20%5Csin%282xy%29]" alt="f(z) = e^{{x^2} - {y^2}}[cos(2xy) + i sin(2xy)] " align="absmiddle" /> analytic?<br /> <br /> b) Find <img title=" f'(z)" src="https://latex.codecogs.com/png.latex?%20f%27%28z%29" alt=" f'(z)" align="absmiddle" /> and its derivative</p>

Explanation / Answer

Analytic Function


A complex function is said to be analytic on a region if it is complex differentiable at every point in . The terms holomorphic function, differentiable function, and complex differentiable function are sometimes used interchangeably with "analytic function"

f(z)=e^{{x^2} - {y^2}}[cos(2xy) + i sin(2xy)]
f(z)=e^{{x^2} - {y^2}}*e^i(2xy)
f(z)=e^{{x^2} - {y^2}}+i(2xy)
f1(z)=e^{{x^2} - {y^2}}+i(2xy)* (2x+i(2y))

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