How to graph abs(z-i) = 2 in the complex plane?
How would I do this? Help plox. :3
How would I do this? Help plox. :3
JB
Favorite Answer
The equation says that the distance from z to i is 2, so the graph is a circle centered at i, with radius 2.
Universalist
Let z = a + bi, then abs(z - i) = sqrt(a^2 + (b - 1)^2) = 2 (as given above). Hence a^2 + (b - 1)^2 = 4 which is a circle with center (0, 1) aka i, and radius 2 in the complex plane. I hope this helps!
isenhower
Complex Plane Grapher
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EDIT: I bumped off those products through fact it wasn't proper to the question. to respond to your question, including infinities to the actual line is performed for a various reason than including a unmarried infinity to the complicated airplane. whilst we upload -infty and +infty to the actual line, we are allowing sequences to continuously converge: in a feeling, a astounding and inferior decrease will continuously exist for any series. it incredibly is significant for many purposes. Now the complicated airplane and the actual airplane have little in easy. The algebraic shape is thoroughly diverse (as a field or a vector area), and as replace into reported above, no finished order exists for the complicated numbers it incredibly is like minded with the prevalent topology. The Riemann sphere is what's frequently a "compactification" of the complicated airplane, and being compact is quite significant. it incredibly is the "smallest" compactification, in a feeling. in case you're taking the assumption of stereographic projection somewhat greater effective, you are able to locate there's a topic the place the actual airplane is adjoined with infinitely many infinities. whilst we challenge the actual airplane onto a sphere, we are able to realize this onto basically one hemisphere. Then antipodal factors are indentified, and we arrive (tremendously lots) on the projective airplane, which has a "line" of infinities. i decide to tension inspite of the undeniable fact that that the main significant element all of those structures have in easy is compactness, a significant assets certainly. As for being a 15-12 months-old female attracted to math, it incredibly is great! proceed to verify and love math, and you will do properly certainly. the main needed element of math is calling questions; by no potential take something with no attention. i'm hoping this helps, Steve