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#1 2008-01-05 23:11:42
- Jai Ganesh
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- 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 thatand
.
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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