Question

Find the values of x and y in the following equation

(x+yi)+(4+9i)=9-4i

A. x = 9 and y = -4
B. x = 5 and y = -13
C. x = -9 and y = 4
D. x = 5 and y = 13

Answer 1

`(x+yi)+(4+9i)=9-4i \\\\x+4+yi+9i=9-4i\\\\x+4+(y+9)i=9-4i\\\\x+4=9 \wedge y+9=-4\\\\x=5 \wedge y=-13 \Rightarrow \text{B}`

Answer 2

B. x = 5 and y = -13

Explanation:

Equating real parts, we have ...

... x + 4 = 9

... x = 9 - 4 . . . . subtract 4

... x = 5

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Equating imaginary parts, we have ...

... yi +9i = -4i

... yi = -4i -9i = -13i . . . . subtract 9i

... y = -13 . . . . . . . . . . . divide by i