Question

Can anyone teach me how to write a complex no. in its trigonometrical or polar form?

Answer 1

Sure, so what do you know about it so far? :)

Answer 2

I know this much: that if there is a complex number (x+iy)
Then its polar form is \[re^{i \theta}.\]where \[r=\sqrt{x^2+y^2}.\]& \[\theta = argument\]& trigonometrical form is \[x+iy=r(\cos \theta+i \sin \theta).\]

Answer 3

I mainly have problem in writing argument of a complex number in its trigonometrical form.

Answer 4

Writing a complex number of the form x + iy in polar coordinates of the form rcos θ + irsin θ is called Polar Form of the Complex Number.

Answer 5

A complex number can be written in any of the following polar forms: rcos θ + irsin θ, r(cos θ + isin θ), or rcis θ, where r is known as modulus and θ is known as argument.

Answer 6

i know that but my problem is other:/

Answer 7

i give you an example
Express the complex number - 5 + 5i in polar form.

Answer 8

If your complex number is of the form
a + ib (I'll use a and b instead of x and y, because I reserve those for rectangular coordinates, I hope you don't mind)

Then your r is as you have written, so there's no problem with that :)

As for your argument
Take the absolute values of a and b
and plug them in here :
\[\tan ^{-1}\frac{|b|}{|a|}\]
Note the result, we'll just call it your angle :) (can't think of a better word)

Now
If BOTH a and b were positive, then your argument is precisely your angle :)
If a is negative and b is positive, then your argument is 180 minus your angle :)
If BOTH a and b were negative, then your argument is 180 plus your angle :)
If a is positive and b is negative, then your argument is 360 minus your angle :)

so, does that help? :)

Answer 9

yes thank u.
My main problem in ur last paragraph is solved
but will u do some examples with me?

Answer 10

@nitz gave you one
Do you want to do it? :)

Answer 11

think of complex number like a point on real plane. And use all trigonometry you know same way like in R2