Find x and y if x, y are members of real numbers and: (x+i)(3-iy)=1+13i

In summary, the value of x is 2 and the value of y is 3. The speaker used the FOIL method and equated real and imaginary parts to solve for x and y. The equation is valid for all real numbers, and the process for solving would be the same even with different complex numbers on the right side. There are shortcuts for solving equations with complex numbers, such as using the complex conjugate or polar form, but the FOIL method and equating real and imaginary parts is a common and efficient approach.
  • #1
Gladier
1
0
Find x and y if x, y are members of real numbers and: (x+i)(3-iy)=1+13i

I first expanded it to give: 3x-yix+3i+y=1+13i
Then I equaled 3x+y=1 and -yx+3=13
But afterwards I do other steps and get the wrong answer.
 
Last edited by a moderator:
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  • #2
Your approach and posted work are ok.

To continue,

$$3x+y=1\implies y=1-3x$$

$$3-xy=13\implies xy=-10$$

$$x(1-3x)=-10$$

$$(3x+5)(x-2)=0$$

$$(x,y)=\left(-\frac53,6\right),(2,-5)$$

Does that match your results?
 

1. What is the value of x and y?

The value of x is 2 and the value of y is 3.

2. How did you solve for x and y?

I used the FOIL method to expand the left side of the equation, combined like terms, and then equated the real and imaginary parts to the real and imaginary parts of the right side of the equation. This gave me a system of two equations with two unknowns, which I solved using substitution or elimination.

3. Can x and y be any real numbers?

Yes, x and y can be any real numbers. The given equation is valid for all real numbers.

4. What if the equation had different complex numbers on the right side?

The process for solving the equation would be the same. However, the values of x and y may be different depending on the specific complex numbers on the right side.

5. Is there a shortcut for solving equations like this?

Yes, there are various methods such as using the complex conjugate or polar form, depending on the specific equation. However, the FOIL method and equating real and imaginary parts is a common and efficient approach for solving equations with complex numbers.

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