5.5. Polar Form of Complex Numbers and Exponential Notation

Try these first

1. 1.

   Express the complex number 1 + i in polar form.

   Hint

   Use the modulus and argument definitions.

2. 2.

   What is the modulus of the complex number z = 3 - 4i?

   Hint

   Remember to square both parts of the complex number.

3. 3.

   What is the polar form of a complex number?

   • z = re^{iθ}
   • z = x + iy
   • z = r(cos θ + i sin θ)

   Hint

   Recall how the polar form is defined.

4. 4.

   The modulus of the complex number z = 3 + 4i is:

   • True
   • False

   Hint

   Can you find the distance from the origin?

5. 5.

   Given a complex number z = 1 + √3i, find its polar form and compute z^6.

   Hint

   Determine modulus and angle carefully, then raise to the sixth power.

6. 6.

   Determine the fourth roots of z = -16 using polar form.

   Hint

   Consider how to find both the modulus and the argument.