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What is the product of 3√2cis(π/12) and 2√5cis(4π/3) ?


___cis(___)

User Moncef
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2 Answers

3 votes

Answer: 18.97cis(4.45)

Step-by-step explanation: I did the test and boy I got this wrong, please learn from my mistake.

What is the product of 3√2cis(π/12) and 2√5cis(4π/3) ? ___cis(___)-example-1
User Esteban Feldman
by
7.8k points
5 votes

Answer:

Did you mean
cos instead of
cis ?

If that's the case, then the answer is:


3√(2) cos((\pi)/(12))*2√(5) cos((4 \pi)/(3)) =6√(10) cos(0.66043941112\pi) \approx -9.16

Explanation:

As you may know:


√(ab) =√(a)* √(b)

So:


3√(2) *2√(5) =3*2*√(2*5) =6√(10)

Now:


cos((\pi)/(4)) =(√(6) +√(2) )/(4) \\\\and\\\\cos((4\pi)/(3) )=-(1)/(2)

So:


cos((\pi)/(12) )*cos((4\pi)/(3) )=((√(6)+√(2) )/(4) )*(-(1)/(2) ) =(-√(6)-√(2) )/(8)

Now, using the inverse cosine:


arccos((-√(6)-√(2) )/(8))=2.074831602=0.66043941112\pi

Therefore, the equivalent expression for the product of 3√2cis(π/12) and 2√5cis(4π/3) is:


3√(2) cos((\pi)/(12))*2√(5) cos((4 \pi)/(3)) =6√(10) cos(0.66043941112\pi) \approx -9.16

User Utpal Kumar
by
8.7k points

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