Question

Express the complex number 5-√3i÷4+2√3 in the form of a+ib ​

Answer 1

Answer:

1−

2

i

5+

2

i

=

1−

2

i

5+

2

i

×

1+

2

i

1+

2

i

=

1

2

−2i

2

5+5

2

i+

2

i+2i

2

=

1+2

5+6

2

i−2

=

3

3+6

2

i

1−

2

i

5+

2

i

=1+2

2

i

Step-by-step explanation:

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Answer 2

Answer:

p(x)=3

2n+2

−8x−9 is divisible by 64 …..(1)

When put n=1,

p(1)=3

4

−8−9=64 which is divisible by 64

Let n=k and we get

p(k)=3

2k+2

−8k−9 is divisible by 64

3

2k+2

−8k−9=64m where m∈N …..(2)

Now we shall prove that p(k+1) is also true

p(k+1)=3

2(k+1)+2

−8(k+1)−9 is divisible by 64.

Now,

p(k+1)=3

2(k+1)+2

−8(k+1)−9=3

2

.3

2k+2

−8k−17

=9.3

2k+2

−8k−17

=9(64m+8k+9)−8k−17

=9.64m+72k+81−8k−17

=9.64m+