Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,257

Complex Numbers - Pre-University level - IV

1. Simplify:

.

2. Prove that

.

3. Prove that

are real and purely imaginary respectively.

4. If

,
prove that

.

5. Find all the values of
(i)

(ii)

(iii)

.

6. If

is the complex cube root of unity and if

,
show that
(i)

(ii)

.

7. If

=1, prove that

.

8. If

, prove that

.

9. If

, prove that

.

10. Solve

---

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.