Unit 2
Unit 2
Hyperbolic function and Logarithm of complex numbers
Question and answer
- Simplify
2. Find the value of 
3. Expand the function 
4. Find out the value of 
5. Prove that 
LHS 
= 
6. Solve 
7. If
then prove that 
……(i)
Squaring both sides
Now, 
……(ii)
Dividing (i) by (ii)
8. Prove that 
Let 
Squaring on both sides
Again 
Taking square root on both side
Now, 
Hence 
9. Separate the real and imaginary part of 
Let 
)….(1)
…..(2)
On adding (1) and (2) we get
Subtracting (1) and(2) we get
Which are the required real and imaginary parts.
10. Find the general value of 
The general value is
11. Separate the real and imaginary part of 
Unit 2
Hyperbolic function and Logarithm of complex numbers
Question and answer
- Simplify
2. Find the value of 
3. Expand the function 
4. Find out the value of 
5. Prove that 
LHS 
= 
6. Solve 
7. If
then prove that 
……(i)
Squaring both sides
Now, 
……(ii)
Dividing (i) by (ii)
8. Prove that 
Let 
Squaring on both sides
Again 
Taking square root on both side
Now, 
Hence 
9. Separate the real and imaginary part of 
Let 
)….(1)
…..(2)
On adding (1) and (2) we get
Subtracting (1) and(2) we get
Which are the required real and imaginary parts.
10. Find the general value of 
The general value is
11. Separate the real and imaginary part of 
