What is i divided by 8+i

(8i+1) / 65

Step-by-step explanation:

To divide the complex number i by 8+i, we will rationalise by multiplying the resulting complex number by the conjugate of its denominator. This can be expressed as;

i/8+i

= i/8+i * 8-i/8-i

= i (8-i) / (8+i) (8-i)

= 8i-i²/64-8i+8i-i²

= 8i-i²/64-i²

Since i² = - 1 in complex notation,

The equation becomes;

8i - (-1) / 64 - (-1)

(8i+1) / 65

(1 + 8i) / 65.

Step-by-step explanation:

When we divide by a complex number we multiply top and bottom of the fraction by the conjugate; this creates a real denominator.

So i / (8 + i) The conjugate of 8 + i is 8 - i, so we have:

i (8 - i) / (8 + i) (8 - i)

= (8i - i^2) / (64 - i^2) Now i^2 = - 1 so we have:

(8i + 1) / (64 + 1)

= (1 + 8i) / 65.