Find all values complex equation

In summary, the conversation discusses solving the equation zc=ec log(z) using the equation z1/n=exp[(1/n) log(z)], where n is an integer. The attempt at a solution involves substituting c=.5-i and z=i, leading to the reduction of the equation to i.5*e-i log(i). The conversation ends with a suggestion to find the possible values of log(i) to continue solving the equation.
  • #1
alexcc17
48
0

Homework Statement


i.5 - i


Homework Equations


zc=ec log(z)

z1/n=exp[(1/n) log(z)], n is in integer


The Attempt at a Solution



letting c=.5-i and z=i so

zc=e(.5-i) log(i) = e.5 log(i)*e-i log(i)

from the second equation I reduced it to:
i.5*e-i log(i) but I'm not sure where to go from there since the second known equation doesn't apply to the e^(-i log(i)) part
 
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  • #2
alexcc17 said:

Homework Statement


i.5 - i


Homework Equations


zc=ec log(z)

z1/n=exp[(1/n) log(z)], n is in integer


The Attempt at a Solution



letting c=.5-i and z=i so

zc=e(.5-i) log(i) = e.5 log(i)*e-i log(i)

from the second equation I reduced it to:
i.5*e-i log(i) but I'm not sure where to go from there since the second known equation doesn't apply to the e^(-i log(i)) part

exp(log(i)*(.5-i)) is a good start. Now figure out what possible values log(i) could have.
 
  • #3
I got it thanks though
 

Related to Find all values complex equation

1. How do I find all the values of a complex equation?

To find all the values of a complex equation, you must first understand the components of the equation. This includes identifying the real and imaginary parts, as well as any constants or variables. Then, you can use algebraic techniques such as substitution or factoring to solve for the values of the complex equation.

2. Can I use the quadratic formula to find all the values of a complex equation?

Yes, you can use the quadratic formula to find all the values of a complex equation. However, the quadratic formula only works for equations in the form of ax^2 + bx + c = 0. If your complex equation does not have this form, you will need to use other algebraic techniques to solve for the values.

3. Are there any specific rules or methods for finding all the values of a complex equation?

There are several rules and methods for finding all the values of a complex equation, including using algebraic techniques like substitution, factoring, and the quadratic formula. Additionally, you can use graphing techniques or software programs to visualize and solve complex equations.

4. Can I use the imaginary unit to find all the values of a complex equation?

Yes, you can use the imaginary unit, denoted by i, to find all the values of a complex equation. The imaginary unit represents the square root of -1 and is often used in complex numbers and equations. It can help simplify calculations and solve for the values of complex equations.

5. Are there any special cases or exceptions when finding all the values of a complex equation?

Yes, there are some special cases and exceptions when finding all the values of a complex equation. For example, if the equation has multiple variables or exponents, the solution may include multiple values or be more complex. Additionally, some equations may have no real solutions, which can be identified by the discriminant being less than 0 in the quadratic formula.

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