Unit – 1
Complex Numbers
Question and answer
- Express in the form of a + ib :
2. find the modulus of
3. If then show that are conjugate complex numbers?
Let
Also
Again
Hence both of them are conjugate to each other.
4. Find the value of
Sol:
5. Find the value of
Sol:
6. If are the roots of the equation .prove that
Sol: If are the roots of the equation
Therefore
So,
}
=
7. Prove that
-
8. Expand the in power of sine
9. Prove that
Sol: Using
10. If z is fifth root of unity i.e. then find all the values of z?
Sol: Given
Therefore roots of z are 1,
Try: find the square root of
11. form the equation whose roots are
Let
Therefore
When ( y - 1 )=0 this gives
by re arranging
Dividing each term by
Therefore
……. (i)
Since
Also
Hence roots of the equation (i) are