Answer:
(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.
Answer:
(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
