Math, asked by mibrahimgazi11, 11 months ago

Find the real numbers x and y such that
x/1+2i+y/3+2i=5+6i/-1+8i​

Answers

Answered by sk940178
11

Answer:

x=1

y=2

Step-by-step explanation:

We are given that \frac{x}{1+2i} +\frac{y}{3+2i} =\frac{5+6i}{-1+8i}

Now, rationalizing the denominator  og all the terms, we get

\frac{x(1-2i)}{5} +\frac{y(3-2i)}{13}= \frac{(5+6i)(-1-8i)}{65} \\

Separating the real and imaginary parts from the above equation, we get,

⇒[[\frac{x}{5}+\frac{3y}{13} ]-[\frac{2x}{5}+\frac{2y}{13}  ]i=\frac{43}{65} -\frac{46}{65} i

Hence, comparing real and imaginary parts of the above equation we get,

\frac{x}{5} +\frac{3y}{13} =\frac{43}{65} ...... (1)

Multiplying 2 in the both sides we get,

\frac{2x}{5} +\frac{6y}{13} =\frac{86}{65} ...... (2)

Again, \frac{2x}{5} +\frac{2y}{13}=\frac{46}{65} ..... (3)

Now, solving equations (2) and (3) we get,

4y/13=40/65

y=2

Again from equation (1), we get, x/5+6/13=43/65

⇒ x/5 =13/65

x=1 .

Hence, the values of the real numbers x and y are 1 and 2 respectively. (Answer)

Answered by awadhutghavade
1

Answer:

x=1

y=2

Step-by-step explanation:

We are given that  

Now, rationalizing the denominator  og all the terms, we get

Separating the real and imaginary parts from the above equation, we get,

⇒[

Hence, comparing real and imaginary parts of the above equation we get,

...... (1)

Multiplying 2 in the both sides we get,

...... (2)

Again,  ..... (3)

Now, solving equations (2) and (3) we get,

4y/13=40/65

⇒ y=2

Again from equation (1), we get, x/5+6/13=43/65

⇒ x/5 =13/65

⇒ x=1 .

Hence, the values of the real numbers x and y are 1 and 2 respectively. (Answer)

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