Complex Numbers and Roots- i Term

Question

(Find the value of X and Y that make each equation true)

 

1. 2x-20i=8-(4y)i

2. 5i-6x=(10y)i+2

 

(Find each Complex Conjugate) 

3. i-3

4. 3i-4

5. 11i

 

6. The impedance of an electrical circuit  is a way of measuring how much the  circuit impedes the flow of energy. The impedance can be a complex number. A circuit is being designed that much have an impedance that satisfies the function f(x)=2x^2-12x+40, where X is a measure of the impedance. Find the zeros of the function.

Answer 1

Answers to questions 1 and 2:

 

1. 2x - 20i = 8 - (4y)i

 

    Equate the real parts and imaginary parts to get                                       2x = 8 and -20 =-4y

 

      So, x = 4 and y = 5

 

2. 5i - 6x = (10y)i + 2

 

    Proceed as in question 1 to obtain -6x = 2 and 5 = 10y

 

                                                   So, x = -1/3 and y = 1/2 

 

   

Answer 2

First part)

 

Bring all the real terms to the left side of the equation.  Bring all imaginary terms to the right side.  Also, align all like terms.

 

2x - 8 = 20i - 4iy                     eq1

-6x - 2 = - 5i + 10iy                  eq2

 

 

Next, we can multiply eq1 by 3.   Keep eq2 as it is.

 

6x - 24 = 60i - 12iy                   eq1

-6x - 2 = -5i - 10iy                    eq2

 

 

Add the equations to eliminate the x terms.

 

-26 = 55i - 22iy

 

 

Subtract 55i on both sides of the equation.

 

-26 - 55i = -22iy

 

 

Divide both sides of the equation by -22i.

 

(-26 - 55i) / -22i = y

 

 

Then substitute this value of y into eq2 to solve for x.  I leave this part to you.

 

 

Second part)

 

conjugate of    -3 + i      is      -3 - i

conjugate of    -4 + 3i    is      -4 - 3i

conjugate of     11i         is     -11i

 

 

Last part)

 

Set f(x) equal to zero and solve for x.  I suggest you use the quadratic formula to sovle for x, since you are likely to have complex roots.