How Do You Convert \( e^{1+j2} \) to Cartesian Form?

In summary, the conversation is about a complex numbers problem and the person is asking for help in expressing 2.91e to the power of 1+j2 in Cartesian form. They have tried solving it in polar form and converting it to Cartesian, and are now seeking assistance using Euler's formula.
  • #1
Silmax
4
0
complex numbers problem...need help

Hi all
Could anyone out there please help me with the solution to this problem.

Express 2.91e to the power of 1+j2 in Cartesian form (x+jy)

Sorry writing it out, but I don't know how to set it out on the computer.


I have tried solving the 1+j2 first then adding this to the real number then working it out in polar form then converting it to Cartesian, but I don't know if this is right.

Any help would be much appreciated.
Thank you
 
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  • #2
You should start by separating the two parts of the complex exponential:

[tex]2.91 e^{1+j2} = 2.91{e^1} {e^{j2}} [/tex]

and then use Euler's formula on the [tex] {e^{j2}} [/tex] part... Does that help?

http://en.wikipedia.org/wiki/Complex_exponential


.
 
  • #3
Thank you

I shall give it a go.
Thank you for your help
 

1. What are complex numbers and why are they important in science?

Complex numbers are numbers that have a real part and an imaginary part. They are important in science because they allow us to solve problems that cannot be solved with only real numbers, such as finding roots of negative numbers or modeling real-world phenomena like electrical circuits and quantum mechanics.

2. How do you add and subtract complex numbers?

To add or subtract complex numbers, you simply combine the real parts and the imaginary parts separately. For example, (3+2i) + (5+4i) = (3+5) + (2+4)i = 8 + 6i. Similarly, (3+2i) - (5+4i) = (3-5) + (2-4)i = -2 - 2i.

3. Can you multiply and divide complex numbers?

Yes, you can multiply and divide complex numbers. To multiply, you use the FOIL method, just like with binomials. For example, (3+2i)*(5+4i) = 15 + 12i + 10i + 8i^2 = 15 + 22i - 8 = 7 + 22i. To divide, you use the conjugate of the denominator to eliminate the imaginary part. For example, (3+2i) / (5+4i) = ((3+2i)*(5-4i)) / ((5+4i)*(5-4i)) = (15+6i-8i-4i^2) / (25-16i^2) = (11-2i) / 41.

4. How do you graph complex numbers on the complex plane?

To graph a complex number on the complex plane, you plot the real part on the x-axis and the imaginary part on the y-axis. For example, the complex number 3+2i would be graphed at the point (3,2). This can help visualize complex numbers and their relationships to each other.

5. What is the difference between a real and imaginary number?

Real numbers are numbers that can be plotted on a number line and have a single value. Imaginary numbers, on the other hand, cannot be plotted on a number line and have two parts, a real part and an imaginary part. Real numbers are used to represent quantities like length, time, and temperature, while imaginary numbers are used to represent quantities like voltage, current, and resistance.

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