What would the set of numbers of the form kz... (1 Viewer)

[Utility]

... look like if k was allowed to vary over all possible complex no.s? Note, z = 3+9i. k = every possible complex no. (& obv. all the purely reals too).

 

[Lieutenant_21]

... look like if k was allowed to vary over all possible complex no.s? Note, z = 3+9i. k = every possible complex no. (& obv. all the purely reals too).

(x+iy)(3+i9)?

 

[Viscass]

... look like if k was allowed to vary over all possible complex no.s? Note, z = 3+9i. k = every possible complex no. (& obv. all the purely reals too).

it would just be every complex number on the complex plane,
k=rcis(theta)
kz means a rotation of theta (for 0<=theta<=2pi)
and a lengthening of r (probably not the best wording) of the ray of z
seeing as both r and theta are unbounded the new modulus and argument can be any value

 

[Utility]

it would just be every complex number on the complex plane,
k=rcis(theta)
kz means a rotation of theta (for 0<=theta<=2pi)
and a lengthening of r (probably not the best wording) of the ray of z
seeing as both r and theta are unbounded the new modulus and argument can be any value

Correct. It forms every complex no. (& thus every real no.).

 

[RealiseNothing]

Correct. It forms every complex no. (& thus every real no.).

A more general way to look at this is you have some number which is within the complex field, and you have some factor that can be any number within the complex field. Obviously the set of would be any number you want within the complex field as we can just let , choose the value of we want, and reverse the process to find a suitable value.

 

[Utility]

Yeah, nice one.