Converting to Polar and Cartesian form

In summary, the conversation discusses the process of converting complex numbers into Cartesian and polar forms. It is recommended to understand the concepts of Cartesian and polar forms, finding the real and imaginary parts of a complex number, and finding the modulus and argument of a complex number before attempting to solve the given equations. The conversation also mentions the use of rationalizing the denominator when dealing with complex numbers in the denominator. It is also suggested to use the trick of multiplying by 1 to eliminate complex numbers in the denominator.
  • #1
SteliosVas
70
0
Mod note: This post with template not used and no effort shown received a warning.

Okay I am totally confused in this.
This is not a homework question but rather one I saw online and was wondering for example how to solve it

The question was -3-i/-8+6i to be expressed into Cartesian form.

Another similar one was -2-2*sqrt(3i) into polar form.

How can I do this?

Can someone actually explain I don't get it fully. I know you usually use Cartesian form but yeah...
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Do you know what polar and cartesian forms are?
Do you know how to find the real and imaginary parts of a complex number?
Do you know how to find the modulus and argument of a complex number?
If the answer to any of the above is "no", then please look them up before returning.
If the answer to all of the above is "yes", then what's the problem?
Please show your best attempt.

Note:
1. search for: "rationalize the denominator"
2. search for: "square root of pi"
 
  • #3
Are these complex numbers or vector components. When you have an i in the denominator, you may treat it as i^-1 which equals i which will help eliminating complex numbers. If it is a vector component, recall x=rcostheta y=rsintheta.
 
  • #4
JohnPrior3 said:
Are these complex numbers or vector components.
It's fairly obvious that they are complex numbers.
JohnPrior3 said:
When you have an i in the denominator, you may treat it as i^-1 which equals i which will help eliminating complex numbers.
This doesn't help if the denominator has a sum of terms in it.
JohnPrior3 said:
If it is a vector component, recall x=rcostheta y=rsintheta.
 
  • #5
you may treat it as i^-1 which equals i
... misplaced a minus sign I think, typo?
Just so people who google here don't get the wrong idea:$$\frac{1}{\sqrt{-1}}=\frac{1}{i}=-i$$ ... it's actually easier to use in the fraction form.

The trick: Since I can multiply by 1 without changing the number, and any number divided by itself is 1, I can do: $$\frac{1}{i} = \frac{i}{i}\frac{1}{i} = \frac{i}{-1} = -i$$ ... see what I did there?

The general form of this trick, when it leaves a real number in the denominator, is called "rationalizing the denominator" (see note post #2).
Hopefully OP will get back to us and supply the needed information.
 

1. What is the difference between polar and cartesian coordinates?

Polar coordinates represent a point in terms of its distance from the origin and the angle it makes with the positive x-axis. Cartesian coordinates represent a point in terms of its distance from the x-axis and y-axis.

2. How do I convert from polar to cartesian coordinates?

To convert from polar to cartesian coordinates, you can use the following formulas: x = r * cos(theta) and y = r * sin(theta), where r is the distance from the origin and theta is the angle in radians.

3. What is the purpose of converting between polar and cartesian coordinates?

Converting between polar and cartesian coordinates allows us to represent points in different coordinate systems and make calculations or graph them in a different way.

4. Are there any limitations to using polar coordinates?

Yes, polar coordinates are limited in their ability to represent certain shapes or curves, such as vertical or horizontal lines. They are also not as useful in certain applications, such as computer graphics.

5. How do I convert a complex number to polar form?

To convert a complex number to polar form, you can use the formula: r = sqrt(a^2 + b^2) where a is the real part and b is the imaginary part of the complex number. The angle theta can be found using the formula: tan(theta) = b/a.

Similar threads

How to find z^n of a complex number
    • Precalculus Mathematics Homework Help
Replies
12
Views
992
I Cartesian to Polar form.... Is it just a transformation of the plane?
    • General Math
Replies
8
Views
1K
Write ##5-3i## in the polar form ##re^\left(i\theta\right)##
    • Precalculus Mathematics Homework Help
Replies
9
Views
2K
Converting standard to polar form
    • Precalculus Mathematics Homework Help
Replies
6
Views
2K
Complex numbers: convert the exponential to polar form
    • Precalculus Mathematics Homework Help
Replies
9
Views
2K
B: Calculate the distance between two points without using a coordinate system
    • Precalculus Mathematics Homework Help
Replies
20
Views
2K
Finding z^4 in Polar & Cartesian Forms
    • Precalculus Mathematics Homework Help
Replies
4
Views
1K
Show proof of point C in the given problem that involves Polar equation
    • Calculus and Beyond Homework Help
Replies
3
Views
123
Solving Plane Equation 3x + 2y -z = 4
    • Precalculus Mathematics Homework Help
Replies
8
Views
1K
How do I convert 2cis(-pi/3)cis(pi/6) into cartesian form?
    • Precalculus Mathematics Homework Help
Replies
6
Views
3K

Hot Threads

Recent Insights

Back
Top