1) Prove that : [cos 0 – i sin 0] 2) For z = -4 + 4i , find z in exponension form. ||

Q: (3) a) Prove that the following functions are harmonic and find for each function its harmonic…

A: Here we have to prove that the given function is harmonic function and also to find it's harmonic…

Q: Evaluate [sin³ a x cos x dx. + C

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Q: Prove that eax (a cos bx +b sin bx) + C. ax cos bxdx %3D a2 + b2

A: ∫eaxcosbxdx=eaxacosbx+bsinbxa2+b2+C

Q: Show that π/2 [*¹2 J₁ (z cos 0)d0 = 1- cos z Z

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Q: tan²(z) cos³(z)dæ

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Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

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Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

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Q: Evaluate cos³ (72) sin(7x)dr / COS³ + C

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Q: O Find the anfidanialtiner Sfaw da for fla)= 18 Cos (6x) 16- Sin? (6x) © fa) = ¿* (, +x) 9 + xe

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: expand the formula for sin(A+B)

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Q: prove that sin(45° + A) sin(45° - A) = 1/2cos2A

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Q: Use complex analysis methods to find T = 6²² 5 I 2π cos 2x 5 + 4 cos x dx.

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Q: a) Describe a strategy that could be used to verify the identity (sin z+ cos z)² =1+ sin (2z). %3D…

A: a) strategy used to verify the identitysinx+cosx2=1+sin2xb) Algebriacally prove the identity…

Q: Compute the trigonometric functions of the complex numbers cos(5+ j8) tanh( 0 – j8)

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Q: Evaluate f(4 cos 0 – 0) de -

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Q: Let z=x+iy be a complex number such that coshz =0. Then Im(tanhz) is equal to * sinycosy…

A: first option is correct answer. Thankyou

Q: Prove the identities: (x sin 0 – y cos 0)² + (x cos 0 + y sin 0)² = x² + y²

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Q: Let f(r) (3sin a + 5 cos z)tan r)tan f (x)-

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