1. Complex integers? Here a and b are integers.
What are the possible values of a and b?

2. Complex integers? Here a and b are integers:
What are the possible values of a and b?
Notes and Solution
Equating real and imaginary parts gives a2 + 2b2 = 9 and –ab = 2.
Since a and b are integers the only possible values are a = 1 and b = -2 or a = -1 and b = 2.

3. Down under
Solve

4. Down under
Solve
Notes and Solution

5. Quadratic shift x2 + 3x + c = 0 has complex roots
x2 + 4x + c = 0 has distinct real roots
c is an integer
What is the value of c?

6. Quadratic shift
x2 + 3x + c = 0 has complex roots ; x2 + 4x + c = 0 has distinct real roots; c is an integer. What is the value of c?
Notes and Solution
The discriminant of x2 + 3x + c is 9 – 4c. Since x2 + 3x + c = 0 has complex roots this is less than 0.
i.e. 9 – 4c < 0 and so
The discriminant of x2 + 4x + c is 16 – 4c. Since x2 + 3x + c = 0 has distinct real roots this is greater than 0. i.e. 16 – 4c > 0 and so c < 4.
Since c is an integer c must be 3.