Below are difficult questions that need to be tackled correctly. provide explanations that are easy to understand.

1.The following point (8, 2/3)needs to be represented into Argand plane. Convert and explain

2.What can we say about the roots of a quadratic equation when the discriminant is less than zero?

3.Determine the value of sin + sin where and are the roots of acos + bsin = c.

4.Given x + i y which is a point on the real axis, determine is mirror image. Explain

5.Determine the value of (a + b) if there is only one common root inx²+ ax + b = 0 and x²+ bx + a = 0

6.Determine the equation formed and whose roots are ²+ 2 and ²+ 2 if the roots of an equation 2x²- 3x - 6 = 0 are and .

7.Determine the value of p and q which are the roots of x²+ px + q =0

8.Suppose equation x²+ 3x + 3 = 0 andx²+ bx + c = 0have one root in common, find sum of b + c.

9.Find the value of |z₁+ z₂+ 3 + 4i| if |z₂| = 3 and |z₁| = 4.

10.Determine the value of z^1/n in accordance to De Moivre's theorem.