Converting complex numbers into cartesian and exponential form

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SUMMARY

The discussion focuses on converting the complex number z = 3 + 5j into Cartesian and exponential forms. The Cartesian form is confirmed as 3 + 5j, representing the point (3, 5) in the xy-plane. The exponential form is derived from the polar coordinates, expressed as \(\rho e^{j\theta}\), where \(\rho\) is the magnitude and \(\theta\) is the angle. The user seeks clarification on these conversions, indicating a gap in their understanding after a four-year hiatus from the topic.

PREREQUISITES
  • Understanding of complex numbers
  • Familiarity with Cartesian coordinates
  • Knowledge of polar coordinates
  • Basic trigonometry for angle calculations
NEXT STEPS
  • Learn how to calculate the magnitude of a complex number
  • Study the conversion from Cartesian to polar coordinates
  • Explore the concept of Euler's formula in relation to complex numbers
  • Practice converting various complex numbers into both forms
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Students in mathematics or engineering courses, educators teaching complex number concepts, and anyone looking to strengthen their understanding of complex number conversions.

shackdaddy836
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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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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.
 
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!
 

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