Query about complex numbers (1 Viewer)

[hayabusaboston]

HI guys
Just wondering, I think all complex numbers can be reduced to a relatively simple a+ib form right? cos if you have multilayered fractions and stuff, and you're asked for the modulus and argument, you can always clean it up to something simple right? but if its something like
(sqrt(2)+3)+i(1+sqrt(2)) then you do modulus= the square root of:
sqrt 2+3 all squared, plus 1+sqrt2 all squared

Right? so what im getting at, you'll always have something simple for a and b in the end which u can easily get modulus and argument from right? argument in the above case is tan^-1 ((1+sqrt2)/(sqrt2+3)) right?

 

[Sy123]

HI guys
Just wondering, I think all complex numbers can be reduced to a relatively simple a+ib form right? cos if you have multilayered fractions and stuff, and you're asked for the modulus and argument, you can always clean it up to something simple right? but if its something like
(sqrt(2)+3)+i(1+sqrt(2)) then you do modulus= the square root of:
sqrt 2+3 all squared, plus 1+sqrt2 all squared

Right? so what im getting at, you'll always have something simple for a and b in the end which u can easily get modulus and argument from right? argument in the above case is tan^-1 ((1+sqrt2)/(sqrt2+3)) right?

Every complex number can be expressed within the rectangular co-ordinate system, if it cant be expressed its some higher order uni thing (qauternion?).
Whether we can humanly find this though is another story, for instance.

Is it possible for us to compute (IN EXACT FORM)

 

[Carrotsticks]

HI guys
Just wondering, I think all complex numbers can be reduced to a relatively simple a+ib form right? cos if you have multilayered fractions and stuff, and you're asked for the modulus and argument, you can always clean it up to something simple right? but if its something like
(sqrt(2)+3)+i(1+sqrt(2)) then you do modulus= the square root of:
sqrt 2+3 all squared, plus 1+sqrt2 all squared

Right? so what im getting at, you'll always have something simple for a and b in the end which u can easily get modulus and argument from right? argument in the above case is tan^-1 ((1+sqrt2)/(sqrt2+3)) right?

Usually, they give you something fairly straightfoward like arctan(pi/3) etc. Anything else would require a proof, in which case they would lead you into it.

 

[Trebla]

Of course any complex number can be expressed in the form a + ib. As long as 'a' and 'b' are real numbers they can as nice or as complicated as anyone wants it to be.