Consider two complex numbers in trigonometric polar form Z

Consider two complex numbers in trigonometric (polar) form: Z = 2(cos 80 degree + ¡ sin 80 degree) and z = 6(cos 200 degree + i sin 200 degree). find the product zw and give your answer in trigonometric form find the quotient z/w and give your answer in trigonometric form (with the argument [0 degree, 360 degree] find (attn .!) z^6 and give your answer in trigonometric form (with the argument [0 degree, 360 degree) find all four complex fourth roots of (attn.!) z and give your answers In trigonometric form

Solution

z = 2(cos80 + i*sin80)

w = 6(cos200 + i*sin200)

a) r1(cos 1+j sin 1)×r2(cos 2+j sin 2) = r1r2(cos[1+2]+j sin[1+2])

zw = 12* (cos80 + i*sin80)* (cos200 + i*sin200) = 12*[cos280 + i*sin280]

b) r1(cos1+j sin1)/r2(cos2+j sin2) = (r1/r2)(cos[12] + j sin[12])

z/w = (1/3)*[cos(120) - i*sin(120)]

c) zⁿ = rⁿ (cos n + i*sin n)

z^6 = 64*(cos 480 + i*sin 480)

d) z^(1/4) = 2^(1/4)*(cos 20 + i*sin20)