3. Prove that sin(z + w) = sin z cos w + cos z sin w for z, w E C. (Warning: the technique we used in Lecture 1 to prove

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3 Prove That Sin Z W Sin Z Cos W Cos Z Sin W For Z W E C Warning The Technique We Used In Lecture 1 To Prove 1 (47.5 KiB) Viewed 16 times

Problem 4 please
3. Prove that sin(z + w) = sin z cos w + cos z sin w for z, w E C. (Warning: the technique we used in Lecture 1 to prove the formula for real inputs does not work for complex inputs (why?). Instead, use the definition of sin and cos in terms of complex exponentials to expand the right-hand side.) 4. Decompose complex sine into real and imaginary components, i.e., write sinz = u + iv where u(x, y) and v(x, y) are real-valued functions. (Hint: problem 3 might be useful.)