complex numbers

Question 1

demoivre’s theorem

Answer 1

(cos x + isin x)^n = cos nx + isin nx

Question 2

z = c + is
z - 1/z = ?

Answer 2

2isin x

Question 3

z = c + is
z + 1/z = ?

Answer 3

2cos x

Question 4

∫ (trig func x)^ n

Answer 4

use z+1/z or z-1/z
then pair to eliminate powers

Question 5

rotation through θ and enlargement by factor r

Answer 5

multiply by re^iθ OE
so can use any complex form

Question 6

translation by vector (x y)

Answer 6

add x + iy OE
so can use any complex form