Question

4. Write the term i-35 in the form of a + ib.
​

Answer 1

Answer:

Answer:

i^{-35}=0+ii

−35

=0+i

Step-by-step explanation:

Given : Expression i^{-35}i

−35

To find : Express expression in the form of a+ib ?

Solution :

Write expression as,

i^{-35}=i^{-34-1}i

−35

=i

−34−1

i^{-35}=i^{-34}\times i^{-1}i

−35

=i

−34

×i

−1

i^{-35}=(i^2)^{-17}\times i^{-1}i

−35

=(i

2

)

−17

×i

−1

We know that, i^2=-1i

2

=−1

i^{-35}=(-1)^{-17}\times i^{-1}i

−35

=(−1)

−17

×i

−1

i^{-35}=\frac{1}{(-1)^{17}}\times i^{-1}i

−35

=

(−1)

17

1

×i

−1

i^{-35}=\frac{1}{-1}\times i^{-1}i

−35

=

−1

1

×i

−1

i^{-35}=-i^{-1}i

−35

=−i

−1

i^{-35}=-\frac{1}{i}i

−35

=−

i

1

Multiply and divide by i,

i^{-35}=-\frac{1}{i}\times \frac{i}{i}i

−35

=−

i

1

×

i

i

i^{-35}=-\frac{i}{i^2}i

−35

=−

i

2

i

i^{-35}=-\frac{i}{-1}i

−35

=−

−1

i

i^{-35}=ii

−35

=i

i^{-35}=0+ii

−35

=0+i

i.e. In the form of a+ib i^{-35}=0+ii

−35

=0+i

Where, a=0 and b=1.

Step-by-step explanation:

hope it help you