important theorems


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De Moivre's Theorem
De Moivre's formula, named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) x and any integer n it holds that The formula is important because it connects complex numbers (i stands for the imaginary unit) and trigonometr..
Probability concepts and probability theorems
Introduction - In our day to day life, we come across many uncertainty of events. We wake up in the morning and check the weather report. The statement could be 'there is 60% chance of rain today'. This statement infers that the chance of rain is more than that having a dry weather. We decide upon ..
Examples:
Derivatives are also used to trace the graphs of different functions. To optimise the value of a differentiable function of practical use, derivatives of the functions are applied. This chapter reveals with many more application of derivatives such as determining the relative error in measurement,..
Introduction
Suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional probability. Baye's theorem is named after the British mathematician Thomas Bayes who published it in a r..
Probability (continued) Introduction
Introduction - From our earlier chapter we know that, in statistical experiments, if the events A and B are independent, then But suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional..
To find the qth roots of a Complex number
One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. We have z = r {cos(2n p + q ) + i sin (2n p + q )} [2n p + q is the general amplitude..
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