source : yahoo.com

## Find the fifth roots of 32(cos 280° + i sin 280°)?

i) Let z = 32(cos 280° + i sin 280°) = 32{cos(k*360° + 280°) + isin(k*360° + 280°)},

where k is an integer.

ii) ==> z^(1/5) = [32{cos(k*360° + 280°) + isin(k*360° + 280°)}]^(1/5)

==> z^(1/5) = 2[cos{(k*360° + 280°)/5} + isin{(k*360° + 280°)/5}]

[Application of De-Moievere’s theorem]

==> z^(1/5) = 2[cos(72k + 56) + isin(72k + 56)]

We can now get the 5 roots, by assigning k = 0, 1, 2, 3 & 4

When k = 0, 1st root = 2(cos 56° + isin 56°)

When k = 1, 2nd root = 2(cos 128° + isin 128°)

When k = 2, 3rd root = 2(cos 200° + isin200°)

When k = 3, 4th root = 2(cos 272° + isin 272°)

When k = 4, 5th root = 2(cos 344° + isin344°)

Root Calculator – This free root calculator determines the roots of numbers, including common roots such as a square root or a cubed root. Estimating an nth Root. Calculating nth roots can be done using a similar method, with modifications to deal with n. While computing square roots entirely by hand is tedious.Found a Mistake? Select text and press Ctrl+Enter.-4(cos210+i sin210) -результат в триг. форме

Find the fifth roots of 32 (cos 280° + i sin 280°). – You can put this solution on YOUR website! i) Let z = 32(cos 280� + i sin 280�) = 32{cos(k*360� + **280**�) + isin(k*360� + **280**�)}, where k is � + 280�)/5}] [Application of De-Moievere's theorem] ==> z^(1/5) = 2[cos(72k + 56) + isin(72k + 56)] We can now get the 5 roots, by assigning k = 0cos(32). Enter angle in degrees or radians Since our angle is between 0 and 90 degrees, it is located in Quadrant I In the first quadrant, the values for sin, cos and tan are positive.matt is standing on top of a cliff 305 feet above a lake. the measurement of the angel of depression to a boat on the lake is 42 degrees. how far is t … he boat from Matt? Question 9 of 10 The first step in the process for factoring the trinomial x2 – 4x – 32 is to: A. find the sum of the factors of 32 B. list all the fa…

3( cos 280° + i sin 280°) 3/4 (cos 70° + i sin 70°) – In fact you should find five fifth roots, using. As may be seen the above root is obtained by putting #n=0# and other roots can be obtained by putting #n=1,2,3" or "4#.there are 5 roots so the angle between each root is 360/5 = 72°. then the other four roots area) Solve for z, i.e. find the fifth roots of -32 I got z= 2cis(Pi/5), 2cis(3Pi/5), 2cis(Pi), 2cis(7Pi/5), 2cis(9Pi/5). b) Label these roots clearly on an Argand diagram. quadratics; z^2-4cos(Pi/5)+4 and z^2-4cos(3Pi/5+4). The question wants linear factors, so I'd then have to write them as linear factors.