Solving Complex Equations: z2+2(1-i)z+7i=0

In summary, the conversation discusses how to identify the coefficients in a quadratic equation and use them to solve for the roots. The coefficients for the equation given are identified as a=1, b=2(1-i), and c=7i. The correct values for a, b, and c are important in solving the equation correctly.
  • #1
KUphysstudent
40
1

Homework Statement


So it is pretty straight forward, solve this.
z2+2(1-i)z+7i=0

Homework Equations


z2+2(1-i)z+7i=0
(-b±√(b2-4ac))/2a

The Attempt at a Solution


So what I would do first is solve 2(2-1)z, I get (2-2i)z=2z-2iz
we now have z2-2iz+7i+2z=0
Now I don't really know what to do because my textbook has two examples, in both z2 is ignored.
first it has z2+2iz-1-i=0 and used a=1, b=2i and c=-1-i
the second example shows z2+2z+4=0 and has 2z=b and ac =4*1

the problem with the two examples is I cannot deduce what will be a, b, and c in my problem.
I mean following the logic of the first example I get 2z = b or -2iz = b and then c = either 7i or 7i + 2z or something completely different.
I tried plugging in the numbers
so:
(-2i ±√(2i^2-4*7i))/2 = (-2i±√(-4-28i))/2

then I tried 2z = b instead of 2i = b
(-2 ±√(2^2-4*7i))/2 = (-2±√(4-28i))/2

I mean this is just guessing and I kept going, what if 7i = b, etc. but it doesn't help me understand what it should be and why, which is really what I want to know and not the solution.
 
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  • #2
We consider equations ##az^2 + bz + c = 0##.

That is, we identify the coefficients in a specific equation with the numbers ##a,b,c.##

We have:

##z^2+2(1-i)z+7i=0 \implies a = 1, b = 2(1-i), c = 7i##.

##z^2+2z+4=0 \implies a = 1, b = 2, c = 4##

and in the last example ##b = 2z## is wrong.
 
  • #3
The ##a## and ##b## of the quadratic equation are the complex coefficients of ##z^2## and ##z## of the equation. ##c## is just the complex constant term. So you can just read them off from the equation. They don't include ##z## or any power of ##z##.
 
  • #4
oh, that explains a lot. Thanks you two I was getting frustrated :)
 
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Related to Solving Complex Equations: z2+2(1-i)z+7i=0

1. What is a Super Simple Complex Equation?

A Super Simple Complex Equation is a mathematical expression that contains both simple and complex components. This means that it may have basic operations like addition and subtraction, as well as more advanced concepts like exponents and logarithms.

2. How is a Super Simple Complex Equation different from a regular equation?

A Super Simple Complex Equation is different from a regular equation in that it contains both simple and complex components, making it more challenging to solve. Regular equations typically only have basic operations and are easier to solve.

3. Why are Super Simple Complex Equations important in science?

Super Simple Complex Equations are important in science because they are often used to describe real-world phenomena and solve complex problems. They allow scientists to model and understand complex systems, such as in physics and chemistry.

4. How do scientists solve Super Simple Complex Equations?

Scientists solve Super Simple Complex Equations using a variety of mathematical techniques, such as substitution, factoring, and the quadratic formula. They may also use computer programs or specialized software to help solve more complicated equations.

5. Are there any real-life applications of Super Simple Complex Equations?

Yes, there are many real-life applications of Super Simple Complex Equations. These equations are used in fields such as engineering, physics, chemistry, and economics to model and solve complex systems and problems. They are also used in technology, such as in computer programming and data analysis.

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