1. The problem is to evaluate the function $f(1) = \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i\right)^1$ and understand its value. 2. The formula used here is the power of a complex number. Since the exponent is 1, the value of the function is simply the complex number itself. 3. The complex number is $\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i$. This can be recognized as a point on the unit circle in the complex plane at an angle of $\frac{\pi}{4}$ radians (or 45 degrees). 4. Since the exponent is 1, the function value is: $$f(1) = \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i\right)^1 = \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i$$ 5. This corresponds to the point $(x,y) = \left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$ on the complex plane. 6. To graph this function for $x=1$, plot the point $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$ in the complex plane, which lies on the unit circle at 45 degrees. Final answer: $$f(1) = \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i$$