Question

The real part of the ratio 5 + i /3 + 4i is 19/25??​

Answer 1

Answer:

sorry this question is not solve

Step-by-step explanation:

but any other questions

Answer 2

Final answer: Yes.      

Given that: We are given 5 + i /3 + 4i

To find: We have to find the real part of the ratio 5 + i /3 + 4i is 19/25

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 3 + 4i. Complex conjugate of 3 + 4i = 3 - 4i

• To simplify the given equation multiply both numerator and denominator with 3-4i. It become,[(5 + i)(3 - 4i)] / [(3 + 4i)(3 - 4i)]

•  (a + ib)(a –ib) = a² + b²

• (3 + 4i)(3 - 4i) = 32 + 42 = 9 + 16 =25

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

                                = ac + iad + ibc - bd

• [(5 + i)(3 - 4i)] become (5 * 3) - (5 * 4i) + 3i - 4i²

          = 15- 20i + 3i + 4

          = 19 - 17i

• So given equation become,

[(5 + i)(3 - 4i)] / [(3 + 4i)(3 - 4i)] = (19 - 17i) / 25

• Imaginary part  = 17i/25

Real part = 19/25, hence proved.

To know more about the concept please go through the links

https://brainly.in/question/12184627

https://brainly.in/question/19588839

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