Question

if x(1+3i)+y(2-i)-5+i³=0 find x+y​

Answer 1

Answer:

x + y = 3

Step by step solution:

We are given that

      x( 1 + 3i ) + y( 2 - i ) - 5 + i³ = 0

⇒           x + 3xi + 2y - yi - 5 - i = 0                     ∵ i³ = i²·i = -i

⇒    ( x + 2y - 5) + ( 3x - y - 1)i = 0 + 0i

By equating real and imaginary parts, we get

x + 2y - 5 = 0      .............(1)

3x - y - 1 = 0            .........(2)  

Multiplying equation (2) by 2 we get

6x - 2y - 2 = 0         ..........(3)

Adding equation (1) and equation (3) we get

    7x = 7

⇒   x = 1

By putting x = 1 in equation (1) we get

    1 + 2y = 5

⇒       2y = 4

⇒         y = 2

And

x + y = 1 + 2 = 3

Thus

x + y = 3