Math Port

MATHS PORTFOLIO ------------------------------------------------- Investigation of Patterns from interlocking Numbers Done by: Foo Shang dong Joshua (Pre-U 1 Integrity) A complicated outlet is a pulp consisting of a existent relegate and an imaginary part. Complex verse are get alongs of the var. a + bi, where a and b are authentic total and i is an imaginary number whose square equals -1. Complex metrical composition extend the idea of the linear number line to the flat convoluted plane by using the x-axis on an Argand plot for the real part and the y-axis to regular the imaginary part. In this expression the complex numbers pill into the ordinary real numbers while extending them in care for to solve problems that would be impracticable with only real numbers. De Moivres Theorem is a formula for calculating powers of complex numbers. De Moivres formula states that for any real number and any integer n, ( cos lettuceine + isin)n = cos(n) + isin(n).

let us get by the commit of 3 examples (z3, z4, z5): Using the ordinal grow regularity z3 1 = 0 z3 = 1 z3 = 1 x cis(0 + 2k) z3 = cis2k z = (cis2k)1/3 = cisk Let k=0, 1, 2 3 set of k is compulsory as Z3 has 3 root z = cis0, cis, cis z = cos0 + isin0, cos + isin, cos + isin z = 1, + i , i By using the De Moivres Theorem, 3 solutions of Z3 = 1 devour been obtained. The roots have been plan on an Argand plot as shown below. The Argand Diagram was plan with the use of software product Geogebra. The roots have been plotted on an Argand Diagram, and lines have been emaciated to connect each of the 3 roots as shown below. Re Im ( , ) (1,0) ( , ) ( , ) ( , ) (1,0) Im Re (1,0) ( , ) ( , ) television channel segments were drawn to join the roots together as shown in the Argand diagram below. The diagram has been label with lines a, b, and c. Upon measurement, it had been found that all 3 lines had the same aloofness (1.73units). This proves that the number formed...If you want to get a full essay, revisal it on our website: Orderessay

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