(silly) question on de moivre's theorem expansion

Suppose I have the following complex number:



Using de Moivre's, I write it as:

$\equiv (\cos \theta + i\sin \theta )^{4} [br][br]\equiv \binom{4}{0}\cos ^{4} \theta(i\sin \theta )^{0} + \cdots + \binom{4}{4} \cos ^{0}\theta \left ( i\sin \theta \right )^{4}$

Now to save the pain of writing out all the sin and cos terms in the binomial expansion step, I've written "i x sin(theta)" as "is" and "cos(theta)" as "c".



Now my question is, is this form allowed in examinations? I write it like this to save time but will the examiner look kindly towards it?

Suppose I have the following complex number:



Using de Moivre's, I write it as:

$\equiv (\cos \theta + i\sin \theta )^{4} [br][br]\equiv \binom{4}{0}\cos ^{4} \theta(i\sin \theta )^{0} + \cdots + \binom{4}{4} \cos ^{0}\theta \left ( i\sin \theta \right )^{4}$

Now to save the pain of writing out all the sin and cos terms in the binomial expansion step, I've written "i x sin(theta)" as "is" and "cos(theta)" as "c".



Now my question is, is this form allowed in examinations? I write it like this to save time but will the examiner look kindly towards it?

definitely
(and if they don't I would go afterwards and smash the "shop" up ...)

calm down dear

Suppose I have the following complex number:



Using de Moivre's, I write it as:

$\equiv (\cos \theta + i\sin \theta )^{4} [br][br]\equiv \binom{4}{0}\cos ^{4} \theta(i\sin \theta )^{0} + \cdots + \binom{4}{4} \cos ^{0}\theta \left ( i\sin \theta \right )^{4}$

Now to save the pain of writing out all the sin and cos terms in the binomial expansion step, I've written "i x sin(theta)" as "is" and "cos(theta)" as "c".



Now my question is, is this form allowed in examinations? I write it like this to save time but will the examiner look kindly towards it?

You should put a line in like: "write $s$ for $\sin \theta$, $c$ for $\cos \theta$" and then it will be fine. (I doubt you'd lose marks for not writing tihs, but it's the "right" way to do it).

definitely
(and if they don't I would go afterwards and smash the "shop" up ...)