Question

(x+iy)/2+3i +2+i/2+3i=9/13(1+i)​

Answer 1

Answer:

x = 6.1

y = 2.9

Step-by-step explanation:

(x+iy)/2+3i +2+i/2+3i=9/13(1+i)​

Let solve each Term individually

(x + iy)/ (2 + 3i)   *  (2 - 3i)/(2 - 3i)

= (2x -3xi + 2yi + 3yi²)/(2² - 9i²)

using i² = -1

= ( (2x - 3y )  + i (2y - 3x) ) /13

Similarly

(2 + i)/(2 + 3i)   * (2-3i)/(2 - 3i)

= (1 +  8i)/13

LHS =

(x + iy)/ (2 + 3i) + (2 + i)/(2 + 3i)

=  ( (2x - 3y )  + i (2y - 3x) ) /13   +  (1 +  8i)/13

= ( (2x - 3y + 1)  + i (2y - 3x + 8) ) /13

RHS

= (9/13) (1/1 + i)  * (1-i)/(1-i)

= (9/13) (1 - i)/(2)

= (9  - 9i)/26

= (9/2 - i9/2)/13

Equating LHS & RHS

2x - 3y + 1 = 9/2

=> 4x - 6y = 7     Eq1

2y - 3x + 8 =  -9/2

=> 4y - 6x = -25

=> 6x - 4y = 25     Eq2

2 * Eq1  - 3* eq2

=> 8x - 18x  = 14 - 75

=> -10x = -61

=> x = 6.1

3 * Eq1  - 2* eq2

=> -10y = -29

=> y = 2.9