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

Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches 2 where f of x equals x plus 3 when x is less than 2 and f of x equals 3 minus x when x is greater than or equal to 2 the limit does not exist. 1 2 5 2. find the indicated limit, if it exists. (2 points) limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1 6 0 5 the limit does not exist. 3. find the indicated limit, if it exists. (2 points) limit of f of x as x approaches 0 where f of x equals 5 x minus 8 when x is less than 0 and the absolute value of the quantity negative 4 minus x when x is greater than or equal to 0 -4 -12 -8 the limit does not exist. 4. use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 4 as x approaches 4 from the left . (2 points) ∞ ; x = -4 -∞ ; x = -4 -∞ ; x = 4 1 ; no vertical asymptotes 5. give an example of a function with both a removable and a non-removable discontinuity. (2 points)