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de1irious
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Is it possible for me to write this complex fraction as a ratio of two sines? Thanks.
[tex]\frac{1-e^{101z}}{1-e^{z}}[/tex]
[tex]\frac{1-e^{101z}}{1-e^{z}}[/tex]
de1irious said:I don't think that works though because sin(z) puts the exponent of e as iz and -iz, not z. For instance, if I plug that into a calculator, it doesn't come out equal. I am trying to factor out the real part, but the ratio will not cancel to the point that I have just sines.
That's pretty standard isn't it? You "rationalize" the denominator by mutltiplying both numerator and denominator by the complex conjugate of the denominator. Exactly what the computations are depends on the particular complex fraction. Do you mean "complex fraction" in the sens "fraction with complex numbers" or "fraction with fractions in the numerator and denominator"?orstats said:A related question I have is can we express the complex fraction as a linear equation of Re()+Im()?
A complex fraction as a ratio of sines is a mathematical expression that involves fractions with trigonometric functions, specifically sine functions, in the numerator and denominator.
To simplify a complex fraction as a ratio of sines, you can use trigonometric identities and properties to rewrite the fraction in a more simplified form. This may involve factoring, cancelling out common factors, and using the reciprocal or quotient identities.
Complex fractions as ratios of sines are important in many fields of math, including calculus, trigonometry, and physics. They are used to solve problems involving waves, oscillations, and periodic functions.
Yes, complex fractions as ratios of sines can be converted into other forms, such as a single fraction with a trigonometric expression in the numerator and a constant in the denominator. They can also be written in terms of other trigonometric functions, such as cosine or tangent.
Complex fractions as ratios of sines can be used to analyze and model real-life phenomena that involve periodic motion, such as the motion of a pendulum or a vibrating string. They are also used in engineering and design to calculate the amplitudes and frequencies of waves in different systems.