Answers>Maths>IB>Article

Finding complex numbers using DeMoivre's Theorem

Find the cube roots of 21/2cis(pi/4)
21/2cis(pi/4+ 2pi k), for every integer k
By DeMoivre:
21/2
1/3cis((pi/4+ 2pi k)/3)321/6cis(pi/12+ 2/3pi *k)
Taking k=0,1,2 gives the three cube roots:z1= 21/6cis(pi/12) (k=0)z2= 21/6cis(3pi/4) (k=1)z3= 21/6cis(17pi/12) (k=2)

LR

Related Maths IB answers

All answers ▸

Consider the infinite geometric sequence 25 , 5 , 1 , 0.2 , ... (a) Find the common ratio. (b) Find (i) the 10th term; (ii) an expression for the nth term. (c) Find the sum of the infinite sequence.


Differentiation from first principles


Find the coordinates of the minimum or maximum of the function f(x) = 3x^2 -2x +9 and determine if it's a minimum or maximum.


How do I derive the indefinite integral of sine?