Divide Write your answer in the form a bi 5 3i2 7i Multip

Divide. Write your answer in the form: a + bi. 5 - 3i/2 + 7i, Multiply and simplify. Assume variables represent positive real numbers. write your answer in the form: a + bi. (squareroot 2x + 5 - squareroot 6)^2 (2 squareroot 3 - i squareroot 3)(squareroot 2 + 3i squareroot 2) Simplify each expression. Assume that all variables

Solution

5. (5 -3i)/(2+7i) = [(5-3i)(2 -7i)] / [ (2+7i)(2-7i)] = (10 - 6i - 35i+21i² )/ (4 - 49i²) = (- 41i +10 - 21)/ ( 4 + 49)=

-11/53 + (-41/53)i [ as (a+b)(a -b) = a² - b² and i² = -1]

6. a. ((2x+5) -6)² = [ (2x+5)]² -2[(2x +5) 6] + (6)² = (2x+5) -26(2x+5) + 6 =[2x +11 -2(12x + 30) ] + 0 i.

b.(23 -i3)(2 +3i2) = 26 -i6 + 6i6 -3i² 6 = 26 +5i6 +36 = 56 +i ( 56)