1. The problem asks to show that a complex number $z$ belonging to the set $EC 1 2 - 2 1 5$ is an imaginary number. 2. First, let's clarify what it means for a number to be imaginary: a complex number $z = a + bi$ is imaginary if its real part $a = 0$ and $b \neq 0$. 3. The notation $EC 1 2 - 2 1 5$ is unclear as a standard mathematical set or expression. Assuming it represents a complex number or a set of complex numbers, we need to identify the real and imaginary parts. 4. Since the problem is ambiguous, let's consider a general complex number $z = x + yi$ where $x$ and $y$ are real numbers. 5. To show $z$ is imaginary, we must show $x = 0$. 6. Without additional context or definition of $EC 1 2 - 2 1 5$, we cannot definitively prove $z$ is imaginary. 7. Please provide clarification or the exact expression for $z$ or the set $EC 1 2 - 2 1 5$ to proceed with the proof.