Prove that the complex exponential function e^(ix) can be expressed in terms of sine and cosine functions.

B) Use Euler's formula to show that the product of two complex numbers in polar form is equal to the product of their moduli multiplied by the sum of their arguments.

C) Show that the complex number z = a + bi can be written in polar form as z = r(cos? + isin?), where r = |z| and ? = arg(z).

D) Use De Moivre's theorem to find the cube roots of the complex number 1 + i.

E) Prove that the sum of the nth roots of unity is equal to zero.

F) Find the value of (1 + i)^6 using polar coordinates

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The detailed answer for the above question is provided below A We can start by using Eulers formula eix cosx isinx Therefore we have eix cosx i sinxei... View the full answer