Question

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


___cis(___)

Answer 1

Answer: 18.97cis(4.45)

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

Answer 2

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`