Operations of Complex Numbers in Polar Form 1. Find the product of z1 = 2/3 (cos60° + i sin60°) and z2 = 9 (cos20° + i sin20°) where 0 ≤ theta ≤ 360°

2. Given z1 = 12 (cos pi/3 + i sin pi/3) and z2 = 3 (cos 5pi/6 + i sin 5pi/6), find z1/z2 where 0 ≤ theta ≤ 2pi

3. Find the quotient of z1 = cos 2pi/3 + i sin 2pi/3 and z2 = 2 (cos pi/12 + i sin pi/12) where 0 ≤ theta ≤ 2pi

Lola says these two expressions have the same value. expression a expression b which explains whether lola is correct?

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)

(co 3) the times that customers spend in a book store are normally distributed with a mean of 39.5 minutes and a standard deviation of 9.4 minutes. a random sample of 25 customers has a mean of 36.1 minutes or less. would this outcome be considered unusual, so that the store should reconsider its displays? no, the probability of this outcome at 0.035, would be considered usual, so there is no problem yes, the probability of this outcome at 0.035, would be considered unusual, so the display should be redone no the probability of this outcome at 0.359 would be considered usual, so there is no problem yes, the probability of this outcome at 0.965 would be considered unusual, so the display should be redone