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polet [3.4K]
3 years ago
15

What is i divided by 8+i

Mathematics
2 answers:
atroni [7]3 years ago
8 0

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

sveta [45]3 years ago
3 0

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.

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However, we have way too many unknowns.

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