Find zw and z/w. Leave your answers in polar form. z = 9(cos 110 degree + i sin

Question

Find zw and z/w. Leave your answers in polar form. z = 9(cos 110 degree + i sin 110 degree) w = 2 cos 210 degree + i sin 210 degree) What is the product? ___ [cos ___ degree + i sin ___ degree] (Simplify your answers. Type any angle measures in degrees. Use angle measures greater than or equal to 0 and less than 360.) What is the quotient? __ [cos __ degree + i sin ___ degree] (Simplify your answers. Type any angle measures in degrees. Use angle measures greater than or equal to 0 and less than 360.)

Explanation / Answer

We will use euler's theorem

z = r (cos + i sin ) = r ei

z = 9 (cos 1100 + i sin 1100) = 9 ei 110

w = 2 (cos 2100 + i sin 2100) = 2 ei 210

zw = 9 ei 110  2 ei 210

zw = 18 ei (110+210)

zw = 18 ei (320)

zw = 18 (cos 3200 + i sin 3200)

z/w = (9 ei 110) / (2 ei 210)

z/w = 4.5 ei (110 - 210)

z/w = 4.5 ei (-100)

z/w = 4.5 (cos -1000 + i sin -1000)

-1000 = -1000 + 3600= 2600

z/w = 4.5 (cos 2600 + i sin 2600)

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