Complex Numbers

1. If (a+ib)(c+id) = (p+iq), prove that

(i)(a²+b²)(c²+d²) = p²+q²

(ii)

2. Solve

3. Show that the points representing the complex numbers 7+9i, -3-7i, and 3+3i form a right-angled triangle on the Argand plane.

4. Solve completely

5. If

, prove that

and

.

6. State and prove De Moivre's theorem.

7. Find all the values of

8. Solve the equation

given that (2-i) is a root of the equation.

9. Solve

10. Find the conjugate of