# APPLYING DE MOIVRES THEOREM PRACTICE PROBLEMS

Applying De Moivres Theorem Practice Problems :

Here we are going to see some practice problems on applying de moivres theorem practice problems

## Applying De Moivres Theorem Practice Problems - Practice questions

(1)  If ω ≠ 1 is a cube root of unity, show that

[(a + b ω + cω2)/(b + c ω + a ω2)] + [(a + b ω + cω2)/(c + a ω + b ω2)]  =  -1

(2)  Show that

(3)  Find the value of

(4)  If 2 cos α  =  x + (1/x) and 2 cos β  =  y + (1/y), show that

(i)  (x/y) + (y/x)  =  2 cos (α - β)

(ii)   xy - (1/xy)  =  2i sin (α + β)

(iii)  (xm/yn) -  (yn/xm)  =  2i sin (mα - nβ)

(iv)  (xmyn) +  1/(xmyn)   =  2 cos (mα + nβ)

Solution

(5)  Solve the equation z3 + 27 = 0.        Solution

(6)  If ω ≠  1 is a cube root of unity, show that the roots of the equation (z −1)3 + 8 = 0 are −1, 1− 2ω, 1− 2ω2

Solution

(7)  Find the value of

(8)  If ω ≠  1 is a cube root of unity, show that

(i) (1 − ω + ω2)6 + (1 + ω − ω2)6  =  128.

(ii) (1 − ω)(1 + ω2)(1 + ω4)(1 + ω8).............(1 + ω2^11)  =  1

Solution

(9)  If z = 2 - 2i, find rotation of z by θ radians in the counter clock wise direction about the origin when

(i)  θ  =  π/3    (ii) θ  =  2π/3    (iii) θ  =  3π/2

Solution

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