Complex Plane?

Question

Plot a point corresponding to z = -3 + 4i in the complex plane and then write an expression in z polar form.

Answer 1

There should be an example from your textbook that looks exactly like this one.

Plotting that out is just like plotting it on x-y plane, with x+yi, so go ahead and plot (-3,4) yourself. You should know how to do this pretty well.

To get it in polar form, you need

- Magnitude (use Pythagorean thm on the point, you get 5)
- Angle (use tangent on the point, you get 127˚ *ops*)

Make sure you know how to get these. Your final answer will be in either of these forms:

r * e^(iθ)

r(cosθ + isinθ)

where r is the magnitude and θ is the angle.

Answer 2

Complex numbers are a concept devolped to better understand the real world and mathematical concepts. Its just a human invented concept.

Complex number has two parts :
1) "Real" parth
2) "Imaginary" part , just treat imaginary as a fancy name for a number that fit into the normal numbers like real numbers, just like calling Mickey's dog "Pluto"

A complex plane also has 2 axis correspondingly a real axis (say a horizontal line) and an imaginary axis (a vertical line). They both meet at a point called origin (represented as 0 + 0i)

Imaginary axis
, | +
, |
, - _____|___________ + Real axis
, | 0 + 0i
, |
, |
, -


Now to plot a real number (one without i atached to it) you would move horizontally along the real axis. If it is a positive number you move right from origin (0 + 0i) in the real axis, if it is a negetive number you move to left of origin (0 + 0i)

For imaginary number (one with i attched to it) you move vertically along imaginary axis. If it is positive you move up from origin (0 + 0i). If its negetive you move down from origin (0+0i)


Now in the particular example : z = -3 + 4i
z is a point in a complex plane which is -3 points aways from origin and +4i poits away from origin. In other words, it is 3 points to left of origin and 4 points up from origin. Located somewhat like this (marked by x)


Imaginary axis
, | +
, x |4i
, - _____|___________ + Real axis
, 3 | 0 + 0i
, |
, |
, -

I am not sure if the figure that I have tried to draw will be correctly displayed ( because yahoo will remove space where it is not necessary to conserve space and hence mess-up the drawing). Hope the explanation should give you an idea.

Answer 3

EDIT: I bumped off those products via fact it wasn't correct to the question. to respond to your question, including infinities to the genuine line is done for a diverse reason than including a single infinity to the complicated airplane. whilst we upload -infty and +infty to the genuine line, we are allowing sequences to continuously converge: in a feeling, a great and inferior shrink will continuously exist for any series. that's significant for many applications. Now the complicated airplane and the genuine airplane have little in complication-loose. The algebraic shape is thoroughly diverse (as a field or a vector area), and as became mentioned above, no entire order exists for the complicated numbers it rather is properly matched with the common topology. The Riemann sphere is what's quite often a "compactification" of the complicated airplane, and being compact is amazingly significant. it rather is the "smallest" compactification, in a feeling. while you're taking the belief of stereographic projection somewhat added, you will see that there's a project the place the genuine airplane is adjoined with infinitely many infinities. whilst we challenge the genuine airplane onto a sphere, we are able to realize this onto in basic terms one hemisphere. Then antipodal factors are indentified, and we arrive (extraordinarily lots) on the projective airplane, which has a "line" of infinities. i decide to rigidity nevertheless that the main ingredient all of those homes have in complication-loose is compactness, a significant sources certainly. As for being a fifteen-3 hundred and sixty 5 days-previous woman interested in math, it rather is great! proceed to income and love math, and you will do properly certainly. the main needed area of math is looking questions; in no way take something with no attention. i'm hoping this permits, Steve

Answer 4

Point is (- 3 , 4)
magnitude = 5
Angle = tan^(-1) 4/3 = 126.9°
Polar form is 5 angle 126.9 °
Second quadrant