Thread: complex numbers

agrument of z is the angle theta such that cos theta= x/z modulus and sin theta = y / z modulus. and it is only defined up to the addition of muliples of 2 pie.

can u exaplin this statement
"it is only defined up to the addition of muliples of 2 pie."

One last question.
express the following complex number in polar form

i
now r =1
cos inverse= 0/2=90 * pie/180= pie /2
sin inverse = 1/2= 30 *pie/180 =pie/6

now answer is e ^ (ipie / 2)

Question is why do we take theta value of pie/2 and not pie/6. i have done other questions as well. some time we take theta value which we get thrrough sin and some times the one we get through coz.WHY IS THAT ...PLZ HELP

For your first question, the wording is a little strange and confusing but what I think they're talking about is that only the part that's left over after a multiple of $\displaystyle 2\pi$ is significant. For example, if you had something like $\displaystyle 7\pi$, well that's just the same as $\displaystyle \pi$ because after you take out $\displaystyle 6\pi$ you have just 1 left.

For the second part, I'm confused as to how you got $\displaystyle sin\theta =1/2$. It should be $\displaystyle sin\theta = 1$ because

$\displaystyle i=(0)+(1)i=cos\theta + isin\theta$

so, $\displaystyle cos\theta = 0$ and $\displaystyle sin\theta =1$

You take the value of theta that works for BOTH equations, in this case $\displaystyle \theta =\pi /2$