Question

The imaginary part of ratio 6 + 71 / 5+ 3i is
1/2.​

Answer 1

Answer:

Yes 6+71/5+3 right answer

Answer 2

Final answer: The imaginary part of ratio 6 + 7i / 5+ 3i is 1/2

Given that: We are given 6 + 7i / 5+ 3i

To find: We have to find the imaginary part of ratio 6 + 7i / 5+ 3i is 1/2

Explanation:

• In order to simplify this equation, we convert the denominator to real. To convert to denominator to real multiply both numerator and denominator with the complex conjugate of denominator.

• The complex conjugate of complex equation a + ib = a - ib

• In given equation the denominator is 5 + 3i. Complex conjugate of 5 + 3i = 5 - 3i

• To simplify the given equation multiply both numerator and denominator with 5-3i. It become [(6 + 7i)( 5-3i)] / [(5+3i)( 5-3i)]

• (a + ib)(a –ib) = a² + b²

• (5 + 3i)(5 - 3i) = 5² + 3² = 25 + 9 = 34

• (a + ib)(c + id) = ac + iad + ibc + bdi² where  i = $\sqrt{-1}$, i² = -1

              = ac + iad + ibc - bd

• [(6 + 7i)(5 - 3i)] become (6*5)-(6*3i)+(7i*5)-(7i*3i)

           = 30 - 18i + 35i -21i²  

           = 30 - 17i + 21

           = 51 - 17i

• So given equation become,

[(6 + 7i)(5-3i)] / [(5 + 3i)(5 - 3i)] = (51 - 17i) / 34

• Real part = 51/34

Imaginary part  = 17/34 = 1/2

Hence proved.

To know more about the concept please go through the links

https://brainly.in/question/54164692

https://brainly.in/question/12184627

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