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#1 2008-01-05 23:11:42

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,476

Pre-University - III

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


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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