Converting complex numbers into cartesian and exponential form

In summary, the conversation discusses determining Cartesian and exponential forms of complex numbers, specifically the number 3+5j. The person asking for help is unsure if this is a pre-calculus problem, but remembers learning it a long time ago. They are struggling with the wording of the question and need help finding the polar coordinates of the given number.
  • #1
shackdaddy836
4
0
Hey, I'm not too sure if this is pre-calc or not because it's in a different course but I think I remember doing this in pre-calc a long time ago...

1. Determine cartesian(z = x + jy) and exponential([itex]\rho[/itex]e[itex]^{j\theta}[/itex]) forms of the following complex numbers:

z = 3 + 5j




2. I have no clue if there are any equations



3. I thought this number was already in cartesian form... other than this, there is no attempt

My professor assumed we already knew this. Problem is that it's been so long since I've done these (about 4 years) that I forgot how to do it. So, I have no idea how to even begin...

I only need help on this one number and then I think I can do the rest successfully.

Thanks
 
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  • #2
You're right. That's already in Cartesian form. You can think of 3+5j is just another way of specifying the point (3,5) in the xy-plane. Do you know how to write that same point in polar coordinates? That's all exponential form really is.
 
  • #3
OK. I think I can find the polar coordinates now. I just got stuck on the wording of his question I guess.

Thanks a ton!
 

1. How do I convert a complex number into cartesian form?

To convert a complex number into cartesian form, you can simply write it in the form a + bi, where a is the real part and bi is the imaginary part. For example, the complex number 3 + 4i would be written in cartesian form as 3 + 4i.

2. What is the formula for converting a complex number into exponential form?

The formula for converting a complex number from cartesian form into exponential form is: r(cos θ + i sin θ), where r is the magnitude or modulus of the complex number, and θ is the angle or argument of the complex number.

3. How do I find the magnitude and angle of a complex number?

To find the magnitude of a complex number, use the formula r = √(a^2 + b^2), where a and b are the real and imaginary parts, respectively. To find the angle, use the formula θ = tan^-1(b/a), where a and b are the real and imaginary parts, respectively.

4. Can a complex number be written in both cartesian and exponential form?

Yes, a complex number can be written in both cartesian and exponential form. They are just two different ways of representing the same number.

5. How do I convert a complex number from exponential form into cartesian form?

To convert a complex number from exponential form into cartesian form, you can use the formula a + bi = r(cos θ + i sin θ), where r is the magnitude and θ is the angle of the complex number. You can then simplify the equation to get the complex number in the form a + bi.

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