Having some trouble on how to apprach these 5 questions :( please help Convert e

Question

Having some trouble on how to apprach these 5 questions :( please help

Convert e3.14159-t- to Cartesian form, then take the natural logarithm of both sides of the equation. Convert l to exponential form, then raise both sides of this equation to the Ith power and simplify. Starting with e (a + b) I= ea-1- eb-1 convert both sides to the Cartesian form. Then, since u + v =I x+y implies u=x and v =y, set the real parts equal to get an identity for cos(gamma+delta). Then set the imaginary parts equal to get an identity for sin(gamma+delta). We know that ea + b-1 eaebI = ea.eb-1 =ea. cos(b) + ea sin(b)1, so if ea + b.I=ea+e1 then a=alpha and b = If ea+bI=e-a + c.1 then b = Given e(r + t-1) =a + b.I express r=R(a,b) and t = T(a,b) as functions of a, b. For example r = In ( a2 + b2) is a function of a, b; but it is not quite the right answer. Given e{r + t-J) =a + b.I express a =A(r,t) and b=B(r, t)as functions of r,t. Hint: e(r+t.l) = er.ev1 is a step in the right direction.

Explanation / Answer

take Log with base e and write I=a+ib

then solve

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