Complex Pairs

The questions below are due on Thursday September 18, 2025; 02:00:00 PM.
 
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Let c and d represent the complex numbers shown by filled dots in the following diagram, where the real and imaginary parts of the complex numbers are shown on the horizontal and vertical axes, respectively, and the circle has a radius of 1.

Below are eight complex-valued functions of c and d. Evaluate each expression without using a calculator, and mark its value on the complex plane with a dot. Note that e represents Euler's number (2.71828...) and c^* represents the complex conjugate of c.

Part a:   c+d

Part b:   c-d

Part c:   cd

Part d:   c^*d

Part e:   c/d

Part f:   c/(1-c)

Part g:   e^c

Part h:   e^d

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