Question

What is the result of multiplication of complex numbers -√3+ i and 1/8(cos 5π/3 + i sin5π/3 )?​

Answer 1

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solution:

cos (5π/3) = cos 300° = cos (360° - 60°)

= cos 60° since cos (360° - x) = cos x.

= 1/2.

sin (5π/3) = sin 300° = sin 360° - 60°)

= - sin 60° since sin (360° - x) = - sin x.

= - √3/2

So

(1/8) (cos (5π/3) + isin (5π/3))

= (1/8)(1/2 - i √3/2)

= (1/16) (1- i √3)

Hence -√3+i and (1/8) (cos (5π/3) + isin (5π/3))?

= (-√3+i)(1/16) (1- i √3)

= (1/16)(-√3+i) (1- i √3)

= (1/16) (-√3 + 3i + i + √3)

= (1/16)4i

= i/4.