Question Video: Solving a Two-Variable Linear Equation with Complex Coefficients | Nagwa Question Video: Solving a Two-Variable Linear Equation with Complex Coefficients | Nagwa

# Question Video: Solving a Two-Variable Linear Equation with Complex Coefficients Mathematics • First Year of Secondary School

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Find the real values of π₯ and π¦ that satisfy the equation π₯ + π¦π = (10 + 4π)Β².

02:40

### Video Transcript

Find the real values of π₯ and π¦ that satisfy the equation π₯ plus π¦π equals 10 plus four π squared.

If we get a complex number into the form π plus ππ, π and π are real numbers. And for us, that means here both π₯ and π¦ are real numbers. We have to take 10 plus four π squared and put it into the format of π plus ππ.

At first glance, you might be tempted to take the square root of both sides. However, once weβre here, we end up with a whole host of other problems and weβre no closer to the format π plus ππ. Instead of doing that, we want to actually square 10 plus four π.

We want to find out what 10 plus four π times 10 plus four π is. We can FOIL these two terms. 10 times 10 equals 100. 10 times four π equals 40π. Four π times 10 equals 40π. And four π times four π equals 16, four times four equals 16, π squared, π times π equals π squared.

We combine our like terms. And now, our equation says π₯ plus π¦π equals 100 plus 80π plus 16π squared. You have to remember that the imaginary number π is equal to the square root of negative one. π squared equals the square root of negative one squared, negative one. π squared equals negative one.

In our equation, in place of π squared, we substitute negative one. And then, we have 16 times negative one equals negative 16. 100 plus 80π minus 16. We can combine 100 and negative 16 to get 84 plus 80π. Now, our equation is in the correct format π₯ plus π¦π equals 84 plus 80π. π₯ equals 84 and π¦ equals 80.

The real values for π₯ and π¦ are 84 and 80.

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