Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.1 Complex Numbers - 8.1 Exercises - Page 363: 6

True

Real numbers are complex numbers of the form $a+bi$ where $b=0$ whereas pure imaginary numbers are complex numbers of the form $a+bi$ where $a=0$ and $b\ne0$. Therefore, real numbers and pure imaginary numbers are dissimilar and no real number can be a pure imaginary number.