What happened to m in your answer?Dousin12 said:1. Give a formula for the values on m such that z^m=z
z=cos(7pi/6)+i*sin(7pi/6)
2. If i use de movires i get
3. m*7pi/6=7pi/6 + k*2pi
But then i get the value that k=12/7, Which is the wrong formula.
The correct answer is 1+12k for k=0,1,2...
You have ##\ m=1+\frac{12}{7}k\,,\ ## & k must be some integer. I suppose from the context of the question that m must also be an integer.Dousin12 said:m*7pi=7pi+k*12pi
m=1+12k/7
Okay, i got closer to the right answer now
Which is the equation wolfram alpha also get if i post my original equation. So it must be something wrong!
1+12k is the correct!
Complex numbers are numbers that consist of a real part and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part with i being the imaginary unit (√-1).
Complex numbers are represented on a graph called the complex plane. The real part is plotted on the x-axis and the imaginary part is plotted on the y-axis. The resulting point is called the complex number's modulus and argument.
Real numbers are numbers that can be plotted on a number line and can be written as a decimal or fraction. Imaginary numbers, on the other hand, involve the square root of a negative number and cannot be plotted on a number line.
Complex numbers are used in a variety of fields including physics, engineering, and statistics. They are particularly useful in solving problems involving electricity and magnetism, as well as in solving algebraic equations and modeling real-world phenomena.
Yes, complex numbers can be added, subtracted, multiplied, and divided just like real numbers. The only difference is that when multiplying complex numbers, the imaginary units are combined using the rule i2 = -1. Division of complex numbers involves finding the complex conjugate of the denominator to simplify the expression.