- #1
DivGradCurl
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Folks, I was just wondering why I can write:
[tex]i^{4/3}=-\frac{1}{2}+i\frac{\sqrt{3}}{2}[/tex]
Regards
[tex]i^{4/3}=-\frac{1}{2}+i\frac{\sqrt{3}}{2}[/tex]
Regards
dextercioby said:Sure,complex exponentiation is multivalued,meaning that "i" can be written in an infinite ways using various arguments of the exponential...But worry about that less and use the formula which (though incomplete,hence inaccurate) was already given...
Daniel.
thiago_j said:Folks, I was just wondering why I can write:
[tex]i^{4/3}=-\frac{1}{2}+i\frac{\sqrt{3}}{2}[/tex]
Regards
Imaginary numbers are numbers that when squared, give a negative result. They are denoted by the letter "i" and are used to represent the square root of a negative number.
The value of i^(4/3) is -1/√3 or -0.57735. This can be simplified to -√3/3.
To solve an equation with imaginary numbers, you can use the properties of exponents and the rules of complex numbers. In this case, we can use the formula i^(4/3) = (i^(1/3))^4 to simplify the equation.
Yes, imaginary numbers have many real-life applications in fields such as engineering, physics, and economics. They are used to represent quantities that involve both real and imaginary components, such as alternating current in electrical circuits.
Imaginary numbers are represented on the complex plane as the y-axis, with real numbers on the x-axis. The complex plane is a useful tool for visualizing and understanding complex numbers and their properties.