Question

Solve the equation for x, y ∈ R
$\frac{x+iy}{2+3i}=7-i$

Answer 1

Answer:

x = 17 and y = 19

Step-by-step explanation:

Hi,

Given that (x + iy)/(2 + 3i) = 7 - i

On cross multiplying by 2 + 3i, we get

( x + iy) = (7 - i)*(2 + 3i)

= (7*2 + 7*3i -i*2 -i*3i)

= (14 + 21i - 2i + 3)

= 17 + 19i

Two complex numbers a + ib = c + id ⇔ a = c and b = d  

Real parts should be equal and Imaginary parts should be  

equal,

Hence x = 17 and y = 19

Hope, it helps !

Answer 2

Answer:

x=17 , y=19

Step-by-step explanation:

(x + iy)/(2 + 3i) = 7 - i

cross multiply

( x + iy) = (7 - i)*(2 + 3i)

= (7*2 + 7*3i -i*2 -i*3i)

= (14 + 21i - 2i + 3)

= 17 + 19i

Hence x = 17 and y = 19