1. Simplify the expression sqrt (4x^2/3y) Show your work

2. Simplify the expression (3-4i) (1+5i) - (2-i) Show your work

3. The formula c=sqrt (a^2 + b^2) represents the length of the hypotenuse of a right triangle with side lengths a and b. Solve the equation for b. Show your work.

1. already simplified

2. Foil the first two sets of parenthesis

(3-4i) (1+5i) = 3 + 15i - 4i - 20i^2 (i^2 = - 1 so - 20i^2 becomes + 20)

3 + 11i + 20 = 23 + 11i

Now subtract (2-i) from 23 + 11i

23 + 11i - 2 + i = 21 + 12i

3. c = sqrt (a^2 + b^2) square both sides

c^2 = a^2 + b^2

c^2 - a^2 = b^2

sqrt (c^2-a^2) = b