To solve the expression (–6 + i) over (–5 + i), we can multiply both the numerator and denominator by the conjugate of the denominator to eliminate the imaginary terms.
The conjugate of –5 + i is –5 - i.
So, we have:
(–6 + i)(–5 - i) / (–5 + i)(–5 - i)
Expanding the numerator and the denominator:
(–6)(–5) + (–6)(–i) + (i)(–5) + (i)(–i) / (–5)(–5) + (–5)(–i) + (i)(–5) + (i)(–i)
Calculating the expanded terms:
30 + 6i - 5i - i^2 / 25 + 5i - 5i - i^2
Since i^2 is equal to -1, we can simplify further:
30 + i + 1 / 25 - 1
Simplifying the numerator and denominator:
31 + i / 24
Therefore, the simplified expression is (31 + i) over 24.
Simplify the expression.
(–6 + i) over (–5 + i)
(1 point)
Responses
(31 + i) over 26
Image with alt text: (31 + i) over 26
(29 + i) over 26
Image with alt text: (29 + i) over 26
(31 + i) over 24
Image with alt text: (31 + i) over 24
(31 + 11i) over 26
1 answer
1 answer