To get really good at changing complex numbers between rectangular and polar forms, try these practice problems:

1. Basic Conversions:

   • Change $3 + 4i$ into polar form.
   • Change $-1 - i$ into polar form.

2. Finding Modulus and Argument:

   • Find the modulus $r$ and argument $\theta$ for $5 + 12i$.
   • Figure out the polar form of $-2 + 2i$.

3. Challenge Problems:

   • Convert $-3 - 4i$ into polar form and check your answer.
   • Change the polar form $5(\cos(\frac{3\pi}{4}) + i\sin(\frac{3\pi}{4}))$ back to rectangular form.

Did you know that more than 70% of students do better at these conversions when they practice a lot?