Using your knowledge of complex numbers, such as De Moivre's and Euler's formulae, verify the trigonometric identities for the double angle.
de Moivre's: (cos(x)+isin(x))n=cos(nx)+isin(nx) set n=2 (cos(x)+isin(x))2=cos2(x)+2isin(x)cos(x)-sin2(x), which, according to de Moivre's cos2(x)+2isin(x)cos(x)-sin2(x)=cos(2x)+isin(2x) We notice that on both the RHS and LHS we have real and complex terms, which means that the real part on one side is equal to the real part of the other, and the same stands for the imgainary bits: cos(2x)=cos2(x)-sin2(x) sin(2x)=2sin(x)cos(x) These identities are the correct ones.
CP
Answered by Cezar P. • Further Mathematics tutor
4966 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸z = 4 /(1+ i) Find, in the form a + i b where a, b belong to R, (a) z, (b) z^2. Given that z is a complex root of the quadratic equation x^2 + px + q = 0, where p and q are real integers, (c) find the value of p and the value of q.
Can you express 3 + 4j in polar form?
The finite region bounded by the x-axis, the curve with equation y = 2e^2x , the y-axis and the line x = 1 is rotated through one complete revolution about the x-axis to form a uniform solid. Show that the volume of the solid is 2π(e^2 – 1)
Given that k is a real number and that A = ((1+k k)(k 1-k)) find the exact values of k for which A is a singular matrix.