Complex Solutions Homework - Find Zeros of Equation

  • Thread starter Firepanda
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Hmm perhaps I have to find the discriminant:Yes, you do.which is -4 + 3iso z = (-(1 + 3i) +- i(sqrt (4 - 3i)))/2:/ doesn't look too correctIn summary, the conversation discusses the solution of a quadratic equation with complex coefficients. The attempt at a solution involves finding the roots using the quadratic formula or by completing the square. However, the equation given does not have complex conjugate roots and thus, the solution is incorrect. The conversation also mentions the need to find the discriminant of the equation in order to solve it.
  • #1
Firepanda
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Homework Statement



http://img238.imageshack.us/img238/1381/complexle5.jpg


The Attempt at a Solution



I figure if i just find 1 zero of the equation i can use its conjugate as the other zero, then I guess it's complete.

I know this:

where a is an element of C (Complex)

(z - a) (z - a(conj)) = z^2 - 2(Re a)z + |a|^2

so.. using this

2(Re a) = 1 + 3i
and
|a|^2 = -1 + 3i/4

But what to do from here?
 
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  • #2
Hmm perhaps I have to find the discriminant:

which is -4 + 3i

so z = (-(1 + 3i) +- i(sqrt (4 - 3i)))/2

:/ doesn't look too correct
 
  • #3
quadratic equation …

This is an ordinary quadratic equation.

Just solve it the ordinary way. :smile:

(The only difficulty is that you'll have to calculate the square root of a complex number.)
 
  • #4
Firepanda said:

Homework Statement



http://img238.imageshack.us/img238/1381/complexle5.jpg


The Attempt at a Solution



I figure if i just find 1 zero of the equation i can use its conjugate as the other zero, then I guess it's complete.
No, that's not true. The two roots of a quadratic equation must be conjugates only if the equation has all real coefficients.

I know this:

where a is an element of C (Complex)

(z - a) (z - a(conj)) = z^2 - 2(Re a)z + |a|^2

so.. using this

2(Re a) = 1 + 3i
but that's impossible: 2(Re a) must be a real number.
Again, the roots of this equation are not complex conjugates.

and
|a|^2 = -1 + 3i/4
Once more, that's impossible. |a| is a real number, its square is a real number.

But what to do from here?
Use the quadratic formula or complete the square.
 
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Related to Complex Solutions Homework - Find Zeros of Equation

1. What is the definition of "complex solutions"?

Complex solutions refer to the solutions of an equation that involve imaginary numbers. These numbers are not real, but are expressed as a combination of the real number system and the imaginary unit 'i' (where i = √-1).

2. How do you find the zeros of an equation with complex solutions?

To find the zeros of an equation with complex solutions, you can use the quadratic formula or factor the equation. When using the quadratic formula, the discriminant (b^2 - 4ac) will be negative, indicating that the roots will involve imaginary numbers. When factoring, the equation will typically have a pair of complex conjugate roots, meaning that the imaginary part will be the same but with opposite signs.

3. Can an equation have only complex solutions?

Yes, an equation can have only complex solutions. This occurs when the discriminant of the quadratic formula is negative, or when the equation cannot be factored. In these cases, the solutions will be purely imaginary numbers.

4. How do you graph equations with complex solutions?

To graph equations with complex solutions, you will need to plot points on a complex plane. The real part of the complex number will be plotted on the horizontal axis, and the imaginary part will be plotted on the vertical axis. The solutions will then be represented as points on the graph.

5. Why are complex solutions important in mathematics?

Complex solutions are important in mathematics because they allow us to solve equations that cannot be solved using only real numbers. They also have applications in many fields, such as engineering, physics, and computer science. In addition, they provide a deeper understanding of the properties and behavior of numbers and equations.

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