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How do you simplify # 1/2(cos 2pi/3 + i sin 2pi/3) times 4(cos (pi/2) + i sin (pi/2))#?

1 Answer

Jan 26, 2017

see below

Explanation:

#1/2 (cos((2pi)/3)+i sin((2pi)/3)) * 4(cos(pi/2)+isin(pi/2)) #

Use the formula #r_1 (cos⁡theta_1+i sin⁡ theta_1 )∙r_2 (cos⁡θ_2+i sinθ_2 )= r_1 r_2 [cos⁡(θ_1+θ_2 )+isin(θ_1+θ_2 )]#

#= 1/2 *4 [ cos (((2pi)/3)+pi/2) +i sin (((2pi)/3)+pi/2)]#

#=2[cos ((7pi)/6) + i sin ((7pi)/6)] #

#=2[-sqrt3/2+i(-1/2)]#

#=-sqrt3-i#

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