Complex Integer z=6e2,5i: Explaining Real & Imaginary Parts

[emutudeng]

z=6*e^2,5i

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.

 

[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.

 

[Ray Vickson]

If you mean e^ix = 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

 

[emutudeng]

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

 

[Ray Vickson]

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

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

 

[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 ?

 

[CAF123]

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 ?

Yes.