Find the following product -5(cos pi/3 +isinpi/3)*2(cos pi/6+ isin pi/6'

I got 10i. is this correct?

cos PI/3= .5

sin PI/3= .866
cos PI/6=.866
sin PI/6=.5

put this into your google search engine
-5(.5+i*.866)*2*(.866+i*.5)=

Oh the magic of Google. Now warning, only use this to check your work

I got -10i

Did you get your answer by expanding
-10((cos pi/3 +isin pi/3)(cos pi/6+ isin pi/6) ?

my 2nd-last line was:
-10( cos π/2 + i sin π/2)

To find the product (-5(cos(pi/3) + i*sin(pi/3))) * (2(cos(pi/6) + i*sin(pi/6))), we can use the formula for multiplying complex numbers:

(a + bi) * (c + di) = (ac - bd) + (ad + bc)i

Let's break down the given expression:

-5(cos(pi/3) + i*sin(pi/3)) can be written as -5*1/2 + (-5*sqrt(3)/2)i
2(cos(pi/6) + i*sin(pi/6)) can be written as 2*sqrt(3)/2 + (1/2)i

Now, let's use the formula to find the product:

((-5*1/2) * (2*sqrt(3)/2)) - ((-5*sqrt(3)/2) * (1/2))
= (-5sqrt(3))/2 - (5sqrt(3))/2
= -10sqrt(3)/2
= -5sqrt(3)

((-5*1/2) * (1/2)) + ((-5sqrt(3)/2) * (2*sqrt(3)/2))
= (-5/4) + (-15/4)
= -20/4
= -5

Therefore, the product is -5sqrt(3) - 5.

It seems like you made an error in your calculation. The correct answer is -5sqrt(3) - 5, not 10i.