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Lillianna Wright
Mathematics
19 August, 09:10
What is i divided by 8+i
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Jazlyn Solis
19 August, 09:14
0
(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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Emanuel Kelley
19 August, 09:18
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(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
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