LCKurtz said:That's it. There's only one z equal to that z.
fauboca said:That is really all there is to it?
LCKurtz said:Maybe you are supposed to write it in a+bi form?
The complex variable $z$ is a number that has both a real part and an imaginary part. It is typically represented as $z = a + bi$, where $a$ is the real part and $bi$ is the imaginary part, with $i$ being the imaginary unit equal to $\sqrt{-1}$.
To find the value of $z$ in a complex equation, you will need to solve for both the real and imaginary parts separately. This can be done by using algebraic methods such as combining like terms and isolating the variable $z$ on one side of the equation.
Complex equations can be represented in various forms, such as algebraic form, polar form, and exponential form. In algebraic form, the equation is written as $z = a + bi$, where $a$ and $b$ are real numbers. In polar form, the equation is written as $z = re^{i\theta}$, where $r$ is the distance from the origin and $\theta$ is the angle from the positive real axis. In exponential form, the equation is written as $z = |z|e^{i\arg(z)}$, where $|z|$ is the modulus (or absolute value) of $z$ and $\arg(z)$ is the argument (or angle) of $z$.
A complex equation can have multiple roots, depending on its degree. To determine if a complex equation has any roots, you can use the Fundamental Theorem of Algebra, which states that a polynomial equation of degree $n$ has exactly $n$ complex roots (counting multiplicities). You can also use the Rational Root Theorem to check for possible rational roots.
Yes, there are several techniques that can be used to solve complex equations. These include factoring, completing the square, using the quadratic formula, and using the method of substitution. Additionally, there are specific techniques for solving equations with special forms, such as equations with conjugate pairs or equations with complex coefficients.