- #1
dan5
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e-z2
where z is a complex number a+ib
where z is a complex number a+ib
Splitting an exponential complex number into real and imaginary parts
- Thread starter dan5
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In summary, an exponential complex number is a number in the form of a^bi, where a and b are real numbers and i is the imaginary unit (√-1). To split an exponential complex number into real and imaginary parts, we use the formula a^bi = a(cos(blna) + isin(blna)). The real part is a*cos(blna) and the imaginary part is a*sin(blna). An exponential complex number can have a negative base, but the result will be a complex number with a non-real real part. The real part represents the horizontal component, while the imaginary part represents the vertical component. Splitting an exponential complex number into real and imaginary parts allows us to visualize the number
- #2
I like Serena
Homework Helper
MHB
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Welcome to PF, dan5! 
Can you calculate -z2?
-z2 should be of the form c + id.
According to Euler's formula, we have ##e^{c+id} = e^c ( \cos d + i \sin d )##.
So the real part is ##e^c \cos d## and the imaginary part is ##e^c \sin d##.
Can you calculate -z2?
-z2 should be of the form c + id.
According to Euler's formula, we have ##e^{c+id} = e^c ( \cos d + i \sin d )##.
So the real part is ##e^c \cos d## and the imaginary part is ##e^c \sin d##.
- #3
dan5
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Ahhh now I see, thanks to you, and to Euler!
What is an exponential complex number?
An exponential complex number is a number in the form of a^bi, where a and b are real numbers and i is the imaginary unit (√-1).
How do you split an exponential complex number into real and imaginary parts?
To split an exponential complex number into real and imaginary parts, we use the formula a^bi = a(cos(blna) + isin(blna)). The real part is a*cos(blna) and the imaginary part is a*sin(blna).
Can an exponential complex number have a negative base?
Yes, an exponential complex number can have a negative base. However, the result will be a complex number with a non-real real part. For example, (-2)^i = cos(ln2) - i*sin(ln2).
What is the difference between the real and imaginary parts of an exponential complex number?
The real part of an exponential complex number represents the horizontal component, while the imaginary part represents the vertical component. Together, they form a point on the complex plane.
Why is splitting an exponential complex number into real and imaginary parts useful?
Splitting an exponential complex number into real and imaginary parts allows us to visualize the number on the complex plane and perform operations such as addition, subtraction, multiplication, and division more easily.
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