# Finding complex solutions from an eqn.

• JC3187
In summary, the conversation is discussing finding all complex solutions to z^{2} + Conjugate:z^{2} = 0. The person has come up with a possible way to solve it, but it does not seem to make sense. They suggest adding more information, such as setting z = 1 + i, and solving for the complex roots.
JC3187
Given z = 1 + i,

Find all complex solutions to z^{2} + Conjugate:z^{2} = 0

I have come up with a way to solving this but it doesn't make any sense.

would it be:
z^{2} + 1-i = 0

z^{2} = -1+i

Solve for all complex roots

then do the same for conjugate squared?

JC3187 said:
Given z = 1 + i,

Find all complex solutions to z^{2} + Conjugate:z^{2} = 0

I have come up with a way to solving this but it doesn't make any sense.

would it be:
z^{2} + 1-i = 0

z^{2} = -1+i

Solve for all complex roots

then do the same for conjugate squared?

Finding all complex solutions to z^2+conjugate(z^2)=0 makes a bit of sense. Adding "when z=1+i" makes it make no sense unless you just want to show (1+i)^2+(1-i)^2=0. Or do you just want to solve (1+i)^2+conjugate(z^2)=0??

Last edited:

## 1. How do you find complex solutions from an equation?

The first step is to rewrite the equation in the form of ax2 + bx + c = 0, where a, b, and c are real numbers. Then, use the quadratic formula x = (-b ± √(b2 - 4ac)) / 2a to solve for x. If the discriminant (b2 - 4ac) is negative, the solutions will be complex numbers.

## 2. What is a complex number?

A complex number is a number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1). Complex numbers have a real part and an imaginary part, and they are represented on a two-dimensional plane called the complex plane.

## 3. How do you know if an equation has complex solutions?

An equation has complex solutions if the discriminant (b2 - 4ac) is negative. This means that the solutions will involve the imaginary unit i and cannot be simplified to real numbers.

## 4. Can a real equation have complex solutions?

Yes, a real equation can have complex solutions. This happens when the discriminant (b2 - 4ac) is negative, indicating that the solutions will be complex numbers. It is important to note that even though the solutions are complex, the equation itself is still considered a real equation because all of the variables and coefficients are real numbers.

## 5. How do you represent complex solutions on a graph?

Complex solutions can be represented on a graph using the complex plane. The real part of the complex number is plotted on the x-axis, and the imaginary part is plotted on the y-axis. The solutions will appear as points on the complex plane, and the distance from the origin to the point represents the magnitude of the complex number.

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