Question

What are the values of x and y that make the equations true?

Equation A

(x + yi) + (4 – 7i) = 3 – 4i

Equation B (x + yi) - (-6 + 14i) = 18 + 2i


In equation A, x= ____ and y= ____


In equation B, x= ____ and y= ____

Answer 1

In equation A, x= -1 and y= 3

In equation B, x= 12 and y= 16

Step-by-step explanation:

Given the expression

(x + yi) + (4 – 7i) = 3 – 4i

We are to find the value of x and y

Expand the equation;

(x + yi) + (4 – 7i) = 3 – 4i

x + yi + 4 – 7i = 3 – 4i

x+4+yi-7i = 3 - 4i

x+4 + (y-7)i = 3-4i

Equate the real part

x+4 = 3

x = 3-4

x = -1

Equate the imaginary part;

y - 7 = -4

y = -4 + 7

y = 3

In equation A, x= -1 and y= 3

For equation B:

(x + yi) - (-6 + 14i) = 18 + 2i

x+yi+6-14i = 18+2i

x+6+(y-14)i = 18+2i

x+6 = 18

x = 18-6

x = 12

Equate the imaginary part;

y - 14 = 2

y = 2 + 14

y = 16

Hence In equation B, x=12 and y= 16

Answer 2

In equation A, x= -1 and y= 3

In equation B, x= 12 and y= 16

Explanation:

Given the expression

(x + yi) + (4 – 7i) = 3 – 4i

We are to find the value of x and y

Expand the equation;

(x + yi) + (4 – 7i) = 3 – 4i

x + yi + 4 – 7i = 3 – 4i

x+4+yi-7i = 3 - 4i

x+4 + (y-7)i = 3-4i

Equate the real part

x+4 = 3

x = 3-4

x = -1

Equate the imaginary part;

y - 7 = -4

y = -4 + 7

y = 3

In equation A, x= -1 and y= 3

For equation B:

(x + yi) - (-6 + 14i) = 18 + 2i

x+yi+6-14i = 18+2i

x+6+(y-14)i = 18+2i

x+6 = 18

x = 18-6

x = 12

Equate the imaginary part;

y - 14 = 2

y = 2 + 14

y = 16

Hence In equation B, x=12 and y= 16