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Is Every complex number is a pure imaginary number?
No. All Complex Numbers are of the form a + bi where a and b are Real Numbers and i is the square root of -1. So only ones where a = 0 are pure Imaginary Numbers.
A complex number might not be a pure imaginary number?
True. Complex numbers have a real part and an imaginary part. If either one of these is zero, the complex number will be a pure real or a pure imaginary.
Is the sum of two pure imaginary numbers always a pure imaginary number?
Yes, the only argument would be the example, i + (-i) = 0. However, many people don't realize that 0 is both a purely real and pure imaginary number since it lies on both axes of the complex plane.
Is an imaginary number always sometimes or never a complex number?
Always. The set of imaginary numbers is a subset of complex numbers. Think of complex numbers as a plane (2 dimensional). The real numbers exist on the horizontal axis. The pure imaginary are the vertical axis. All other points on the plane are combinations of real and imaginary. All points on the plane (including imaginary axis and real axis) are complex numbers.
Is 5i a complex number?
Yes it is. All pure imaginary numbers (such as 5i) as well as all real numbers and any combination of real & imaginary (by adding, subtractin, multiplying, dividing) makes a complex number.
