LCKurtz said:Don't you get ##z^2=-1\pm i##? Do you know how to find the square roots of a complex number? That would give you your four roots.
Complex numbers are numbers that have both a real and imaginary component. They are typically written in the form a + bi, where a is the real part and bi is the imaginary part (with i representing the square root of -1).
To find the complex roots of a quadratic equation, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. This formula will give you two complex solutions for x, which represent the two roots of the equation.
Yes, complex roots can be irrational. In fact, they are often irrational since the square root of a negative number is typically irrational.
Complex numbers can be graphed on a coordinate plane called the complex plane. The real component is plotted on the horizontal axis and the imaginary component is plotted on the vertical axis. The point where the two components intersect represents the complex number on the plane.
Finding complex roots can be useful in solving various mathematical problems, such as finding solutions to quadratic equations or analyzing the behavior of complex systems. They also have applications in fields such as engineering, physics, and economics.