A complex number is a number that consists of both a real part and an imaginary part. It is written in the form a + bi, where a is the real part and bi is the imaginary part (with i being the imaginary unit).
A complex number is considered purely imaginary if it has no real part, meaning that the real part is equal to 0. This means that the number is solely made up of the imaginary part, which is a multiple of the imaginary unit i.
In order to determine if a complex number is purely imaginary, you can check if the real part of the number is equal to 0. If it is, then the number is purely imaginary. Additionally, if the number is in the form of ai (where a is a real number), then it is also considered purely imaginary.
The significance of this equation being purely imaginary is that it has no real solutions. This means that when solving for w, you will only get complex solutions in the form of ai. This can be useful in certain mathematical problems and applications.
In order to solve this equation, you can use the quadratic formula. The solutions will be in the form of ai, where a is the square root of the discriminant (b^2-4ac) and i is the imaginary unit. Once you find the two complex solutions, you can substitute them back into the equation to verify that they satisfy the original equation.