Elementary Calculus

Homework 6 - Complex Numbers in Polar Form Name & ID:

Polar → Rectangular Conversion

Suppose we have a complex number expressed in polar form and we want to express it in rectangular form. (That is, we know r and θ and we need a and b.) Referring to the figure we see that we can use the formulas:

Rectangular → Polar Conversion

On the other hand, suppose we have a complex number expressed in rectangular form and we want to express it in polar form. (That is, we know a and b and we need r and θ.) We see that we can use the formulas:

Exercise

Q1. Represent 1+ i3 ​​​ graphically and write it in polar form.

Q2. Represent 2 ​​​− i√​2​​​ graphically and write it in polar form.

Q3. Represent graphically and give the rectangular form of 6(cos 180∘ + isin 180∘)

Q4. Represent graphically and give the rectangular form of 7.32∠−270​∘​​

Q5. Convert the complex number 5 + 2 i to polar form.