Complex integer

1. Sep 16, 2012

emutudeng

z=6*e2,5i

Can anyone explain me ? The imaginary part = 3,59 and real part = -4,81

I tried e(x) = cos x + i sin x, but it does not help me.

2. Sep 16, 2012

CAF123

The complex number $z$ can be expressed in the form $z = r(\cos(θ) + i\sin(\theta)),$ where $z = re^{i\theta}.$ As long as theta is in radians, you should be able to read off the real and imaginary parts.

3. Sep 16, 2012

Ray Vickson

If you mean eix = cos(x) + i*sin(x), then that certainly gives you the correct answer; here you need to use x = 2.5 (N. American style), or x = 2,5 (Euro style).

Note, however, that the given answers are incorrect as exact statements; they are only approximations to the true values, which are approximately
real part ≈ -4.806861693281602289001016742804109986572
and
im part ≈ 3.590832864623738964311128213116973630222
to 40-digit accuracy. No matter how many digits we use we will never be able to write down the exact value.

RGV

4. Sep 16, 2012

emutudeng

How do I calcuate the values if x=2,5 ?

5. Sep 16, 2012

Ray Vickson

What is stopping you from calculating cos(2,5) and sin(2,5)? (Remember, though, that the '2,5' is in radians, not degrees.)

RGV

6. Sep 16, 2012

emutudeng

okey tnx, i undrestood, but i have one other question that if there is no number in the middle for example z=e-5i then r = 1 ?

7. Sep 17, 2012

Yes.