AllShawn
AllShawn AllShawn
  • 08-03-2022
  • Mathematics
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Find the quotient of z1 by 22. Express your answer in trigonometric form
HELP ASAP

Find the quotient of z1 by 22 Express your answer in trigonometric form HELP ASAP class=

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LammettHash
LammettHash LammettHash
  • 08-03-2022

Condense z₁ and z₂ into their exponential forms:

z₁ = 3 (cos(π/4) + i sin(π/4)) = 3 exp(i π/4)

z₂ = 7 (cos(3π/8) + i sin(3π/8)) = 7 exp(i 3π/8)

Then the quotient of z₁ and z₂ is

z₁ / z₂ = 3/7 exp(i (π/4 - 3π/8)) = 3/7 exp(-i π/8)

and in trigonometric form,

z₁ / z₂ = 3/7 (cos(-π/8) + i sin(-π/8))) … … … D

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