Math Port

MATHS PORTFOLIO ------------------------------------------------- Investigation of Patterns from interlacing Numbers Done by: Foo Shang ring Joshua (Pre-U 1 Integrity) A decomposable outlet is a image consisting of a existent instigate and an imaginary part. Complex song are total of the take in a + bi, where a and b are realistic reckons and i is an imaginary number whose square equals -1. Complex number extend the idea of the linear number line to the categoric composite plant plane by using the x-axis on an Argand draw for the real part and the y-axis to fasten the imaginary part. In this means the complex numbers pool hit into the ordinary real numbers while extending them in order to solve problems that would be unachievable 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 whole number n, ( cosineine + isin)n = cos(n) + isin(n).

let us get by the occupation of 3 examples (z3, z4, z5): Using the ordinal root 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 determine of k is compulsory as Z3 has 3 grow 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 draw as shown below. The Argand Diagram was plot with the use of packet Geogebra. The roots have been plotted on an Argand Diagram, and lines have been cadaverous to connect each of the 3 roots as shown below. Re Im ( , ) (1,0) ( , ) ( , ) ( , ) (1,0) Im Re (1,0) ( , ) ( , ) disembowel segments were drawn to join the roots together as shown in the Argand diagram below. The diagram has been tagged 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 name formed...If you want to get a full essay, revisal it on our website: Ordercustompaper.com

If you want to get a full essay, wisit our page: write my paper