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You write e^iπ and only the i ends up in the exponent. If you've ever written LaTeX, you've done this. In Corca you select iπ, right-click, and move it to the exponent.

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To differentiate ∛x, you first rewrite it as x^(1/3). Select it, right-click, and pick Change notation. It switches in place, and you carry on from there.

(x² − 1)/(x − 1) looks like it should simplify, and it does. Select the top, right-click, and pick factor. It becomes (x − 1)(x + 1), and you can see the x − 1 that cancels.

Expanding (a + b)³ by hand is where a coefficient usually goes missing. Right-click it, pick expand, and you get a³ + 3a²b + 3ab² + b³.

You write "where theta is the launch angle" in plain text. Select theta, right-click, and convert it to a variable, so it becomes θ. Then link "launch angle" to θ, and months later you still know what θ is.