Question

Solve (3-4i)(x-yi)=1+0.i for real numbers x and y,

Answer 1

Step-by-step explanation:

(3-4i)(x-yi)=1+0.i

3x-3yi-4xi+4yi²=1+0.i

3x+4y(-1) - i(3y+4x)=1+0.i

(3x-4y) - i(3y+4x) =1+0.i

on comparing the sides

3x-4y=1. ......(i)

and

4x+3y=0 ...........(ii)

multiplying 3 by (i) and 4 by (ii) and adding them

9x-12y=3

16x+12y=0

15x= 3

x=1/5

from (i)

3/5 -4y=1

3/5-1=4y

taking LCM

(3-5)/5=4y

-2/5=4y

y= -2/20

y= -1/10

Hope it helps....