Find the modulus of 1 + i 1 − i − 1 − i 1 + i

NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 47

Total: 52

Find the modulus of

1+i

1−i

−

1−i

1+i

Solution:

We have,

1+i

1−i

−

1−i

1+i

=

(1+i)2−(1−i)2

(1−i)(1+i)

=

(1−1+2i)−(1−1−2i)

1+1

=

2i+2i

2

=

4i

2

= 2i
∴ |

1+i

1−i

−

1−i

1+i

| = √22 = 2

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