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What you have here is correct:

2*e^35°i = 2*e^(35*(pi/180))i = 2*e^0.611i = 2*cos(0.611)+2*sin(0.611)i
= 1.638+1.147i

You might note that both:
       abs(1.638+1.147i)=2  and abs(-1.807-0.856i)=2

Also in RECTANGULAR, DEGREES, APPROXIMATE on my calculator I get:

          (-8)^(1/3)  =   1.0000+1.7321*i

This is one of the third roots of  -8 not the principal root.

In  REAL, DEGREES, APPROXIMATE on my calculator I get:

        (-8)^(1/3)  =  -2

This is the principal third root of -8.

There is a "bug" in the TI-92, no question.

There is also a "bug" on my TI-85 as well:

I get using DEGREE ( on the TI-85):

        2*e^((0,35)) = (-1.8074,-.8564)

In RADIAN:

        2*e^(35*pi/180*(0,1)) = (1.6383,1.1472)

On my new TI-86 I get the same results as with my TI-85.
So there is a "bug" on the TI-86 as well.

It seems that the programmers, way back when, did not take the
correct "branch cut" when they programmed that portion of the calculator.
Maybe the "bug" was past on. The old TI-59 calculator had some "bugs"
with "branch cuts" as well. An incorrect "branch cut" is when
an incorrect "inverse" is taken. for example the "inverse" of z^3
has three branchs or inverses in complex numbers, that is 3 cube roots.
x^2 has two branchs or inverses, that is 2 square roots. The exponential
function has an infinite number of inverses. You can see this in the
example:

                e^(z) = -1

          (pi)*i is one solution (Euler's famous identiy)

          k*(pi)*i  for k an odd integer is the full solution.

When doing calculations envolving exponents logarithms are used.
There is no problem as long as the exponent is real and the
base is positive. Other cases can cause big problems. Some may
think this "branch cut" business does not apply here, but it
does. This in not an easy idea to translate into code and has caused
problems for progammers in the past, me included.

This is a very good example of why we must not trust computers
and calculators completly, even when something has been around
as long as the TI-85.

In RADIAN mode things seem ok. In DEGREE mode there seems to be problems
on all three calculators.

Good Luck

Gary Wardall