How to expand exponential of symbolic expression

Basically i have a huge expression that has a lot of exp((a+bi)*t) terms.

Where a and b are numeric.

What i want is to separate out exp(bi*t) so that i can expand it to cos(bt)+isin(bt). How do i do this?

Answer 1

[Sanil Mhatre]

Input

syms b t
rewrite(exp(bi*t),'sincos')

Output

cos(b*t) + sin(b*t)*1i  end

Answer 2

[Azzi Abdelmalek]

Why are you expecting exp(2*t)*exp(3i*t) ?

2*t and 3*i*t are the same degree

Try this

syms t
q=exp((*t+3i*t^2)
expand(q)

% Result

exp(2*t)*exp(t^2*3*i)

Answer 3

[Walter Roberson]

exp(2*t)*exp(3i*t) expanded is exp(t)*exp(t)*exp(i*t)*exp(i*t)*exp(i*t) . Then automatically gather the identical terms to get exp(t)^2 * exp(i*t)^3 . There is no reason to expect that exp(2*t) * exp(3*i*t) would be given instead when you use expand()