Question

(2
6. If a + b = 1, prove that
1 + b + ia/1+b- is =b+ia​

Answer 1

Answer:

Correct option is

C

b+ia

The value of

1+b−ia

1+b+ia

=

(1+b−ia)(1+b+ia)

(1+b+ia)

2

=

(1+b)

2

+a

2

1+b

2

−a

2

+2iab+2b+2ia

=

1+b

2

+2b+a

2

1+2b+b

2

−a

2

+i(2ab+2a)

=

2+2b

a

2

+b

2

+2b+b

2

−a

2

+i2a(1+b)

=

2(1+b)

2b

2

+2b+i2a(1+b)

=

2(1+b)

2b(1+b)

+i

1+b

a(1+b)

=b+ia