1. The problem is to evaluate and understand the function $f(1) = \left(\frac{12}{17} + \frac{13}{17}i\right)^1$. 2. The formula used here is the power of a complex number. Since the exponent is 1, the function simply returns the complex number itself. 3. Important rule: Any number raised to the power of 1 is the number itself. 4. Therefore, $$f(1) = \left(\frac{12}{17} + \frac{13}{17}i\right)^1 = \frac{12}{17} + \frac{13}{17}i$$ 5. This is a complex number with real part $\frac{12}{17}$ and imaginary part $\frac{13}{17}$. 6. To graph this on the complex plane, plot the point at $(\frac{12}{17}, \frac{13}{17})$. Final answer: $$f(1) = \frac{12}{17} + \frac{13}{17}i$$