Please show steps and answers in good readable handwriting

100.50. Simplify expression with complex numbers. Write the answer in form a+bi, where a and b are real numbers. (6- 4i)(5 9i) 200.50. Simplify expression with complex numbers. Simplify. Write the answer in form a+bi, where a and b are real numbers. (5 4i) 300.5). Simplify complex number (i 1). 107 400.5). Solve quadratic equation 15x 3x 3 5. Solve quadratic equation (the answer might involve i value): 2x2 2x 5 0 6. Find coordinates of vertex, determine if the function has minimum or maximum value and find that value: f(x) 32x2 10x 5

Solution

( 6 - 4i ) ( 5 + 9i )

applying foil method to multiply

6* 5 + 6* 9i - 4i*5 - 9i* 4i

30 + 54i - 20i - 36i^2

combining like terms

30 + 34i - 36i^2

i^2 = -1

30 + 36 + 34i

34i + 66