﻿ Class 11 NCERT Math Solution
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TOPICS
Miscellaneous

Example-1 :-

Solution :-
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Example-2 :-  Find the modulus and argument of the complex numbers:

Solution :-
```(i) We have, (1+i)/(1-i)
= (1+i)/(1-i) x (1+i)/(1+i)
= (1+i²+2i)/(1-i²)
= (1-1+2i)/(1+1)
= 2i/2
= i
= 0 + i

Hence, z = 0 + i
Now, 0 = r cos θ, 1 = r sin θ
By squaring and adding, we get
r2 cos2 θ + r2 sin2 θ = 02 + 12
r2 (cos2 θ + sin2 θ) = 0 + 1
r2 (cos2 θ + sin2 θ) = 1
r x 1 = √1
r = 1
Modulus = 1

Therefore, 0 = r cos θ and 1 = r sin θ
cos θ = 0 and sin θ = 1, which gives θ = π/2
Argument = π/2
```
```(ii) We have, 1/(1+i)
= 1/(1+i) x (1-i)/(1-i)
= (1-i)/(1-i²)
= (1-i)/(1+1)
= (1-i)/2
= 1/2 - i/2

We have, z = 1/2 - i/2
Now, 1/2 = r cos θ, -1/2 = r sin θ
By squaring and adding, we get
r2 cos2 θ + r2 sin2 θ = (1/2)2 + (-1/2)2
r2 (cos2 θ + sin2 θ) = 1/4 + 1/4
r2 (cos2 θ + sin2 θ) = 1/2
r x 1 = 1/√2
r = 1/√2
Modulus = 1/√2

Therefore, 1/2 = r cos θ and -1/2 = r sin θ
cos θ = 1/√2 and sin θ = -1/√2, which gives θ = -π/4
Argument = -π/4
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Example-3 :-

Solution :-
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Example-4 :-

Solution :-
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Example-5 :-  Convert the complex number

Solution :-
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