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Prove the following formulas, where u, v, z are complex numbers and z = x +iy. a....

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Advance Math

Prove the following formulas, where u, v, z are complex numbersand z = x +iy.

a. sin(u+v) = sin u cos v + cos u sin v.

b. cos(u+v) + cos u cos v - sin u sin v.

c. sin^2 z + cos^2 z = 1.

d. cos(iy) = cosh y, sin (iy) = i sinh y.

e. cos z = cos x cosh y - i sin x sinh y.

f. sin z = sin x cosh y + i cos x sinh y.

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