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# Advanced Math/Partial Differential Equations comprising of complex numbers.

Question
Dear Prof Scott

Can Partial Differential Equations comprise of complex numbers?

Thanks
Prashant

Yes, and I'll give a simple one.

It can something as simple as f' - if = 0.
In that case, f(x) = Ce^(ix).
Yes, just remember to put C in if there are no other initial conditions.

We could even have the initial condition be f(0) = i.

Then the solution would be f(x) = ie^(ix).

Perhaps we could have the initial condition of f(i) = 1.

Then the solution would be f(x) = e^(1+ix) since the exponent would be 1 + i*i = 1 - 1 = 0,
and e^0 = 1.

Then again, some say this is just imaginary ...
but I say, it can get complex!

For example, if f(0) = 1 + i, the solution would be f(x) = (1+i)e^(ix).

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Prof Scott Thanks. Prashant

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#### Scott A Wilson

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