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Solve for all possible values of the real numbers xand yin the following equations. (2x-3y-5)+i(x+2y+1)=0

Short Answer

Expert verified

The answer is obtained:

x=1,y=-1

Step by step solution

01

Given information

It is given that 2x-3y-5+ix+2y+1=0.

02

Definition of a complex number

Every complex number can be expressed as:

z=a+bi

Whereaandbare both real numbers, z is the complex number, and i is known as iota, which makes z a complex number.

03

Begin by stating the given information

State the given information:

2x-3y-5+ix+2y+1=0

04

Equate like terms

Equate like terms from both sides:

2x-3y=5x+2y=-1

05

Solve the two equations to find the solutions

Multiply the second equation by2and subtract it from the first equation:

2x-3y=52x+4y=-2

Continue evaluation as:

-7y=7y=-1and2x=5+3-1x=1

Thus, the final answer is obtained:

x=1,y=-1

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