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## 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°)

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Cameron has a bag that contains one silver (S) and one gold (G) marble. – Find. Math Help Please. What are the ratios for sin A and cos A? The diagram is not drawn to scale. Triangle Description- AB = 29 AC = 20 BC – 21 A. sin A Which expression is the is a fourth root of -1+i sqrt3 1. the fourth root of 2 (cos(280 degrees)+i sin(280 degrees)) 2.the fourth root of 2 (cos(30…cos(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.It will also find local minimum and maximum, of the given function. The calculator will try to simplify result as much as possible. 5 . Supported functions: sqrt, ln, e (use 'e' instead of 'exp'), Trigonometric functions: sin cos tan cot sec csc Inverse trigonometric functions: acos asin atan acot asec acsc…