Question

Express 1+i in the form R(cos(theta)+isin(theta))=Re^i(theta).

Answer 1

you need \(r=\sqrt{a^2+b^2}\) and also \(\theta\) which in this case is \(\tan^{-1}(\frac{b}{a})\)

Answer 2

But what's a and b?

Answer 3

\[1+i\\a+bi\]

Answer 4

Wait a minute, please don't leave. Let me do the work.

Answer 5

ok

Answer 6

Remember that 1 can hide.
\(1+i\implies 1+1i\)

Answer 7

But is it always theta=tan^-1 (b/a) for every problem?

Answer 8

no

Answer 9

Then how do I know it's tan^-1 (b/a)?

Answer 10

you don't really need it for the problem because it should be entirely obvious what \(\theta\) is in this example
look at the picture

Answer 11

is it clear what \(\theta\) is here ?

Answer 12

Okay, thanks, guys.

Answer 13

should also be clear what the hypotenuse is too
that is \(r\)