Test Objectives
  • Demonstrate the ability to find the sum of two complex numbers graphically
  • Demonstrate the ability to convert a complex number from rectangular form to polar form
  • Demonstrate the ability to convert a complex number from polar form to rectangular form
Polar Form of Complex Numbers Practice Test:

#1:

Instructions: Find the sum of the two complex numbers graphically.

$$a)\hspace{.1em}(7 + 4i) + (-5 + 6i)$$

$$b)\hspace{.1em}(-7 - 7i) + (6 - 4i)$$


#2:

Instructions: Convert each from polar form to rectangular form.

$$a)\hspace{.1em}5\left(\text{cos}\frac{π}{4}+ i \hspace{.1em}\text{sin}\frac{π}{4}\right)$$

$$b)\hspace{.1em}3\left(\text{cos}\frac{7π}{6}+ i \hspace{.1em}\text{sin}\frac{7π}{6}\right)$$


#3:

Instructions: Convert each from rectangular form to polar form.

$$a)\hspace{.1em}{-\sqrt{6}}+ i\sqrt{6}$$

$$b)\hspace{.1em}2 + 2i\sqrt{3}$$


#4:

Instructions: Convert each from rectangular form to polar form.

$$a)\hspace{.1em}{-3\sqrt{3}}+ 3i$$

$$b)\hspace{.1em}\frac{3\sqrt{3}}{2}- \frac{3}{2}i$$


#5:

Instructions: Convert each from rectangular form to polar form.

$$a)\hspace{.1em}{-\frac{\sqrt{21}}{2}}+ \frac{3\sqrt{7}}{2}i$$

$$b)\hspace{.1em}{-3}- 3i$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}2 + 10i$$ Sketching the parallelogram as the resultant of (7 + 4i) + (-5 + 6i)

$$b)\hspace{.1em}-1 - 11i$$ Sketching the parallelogram as the resultant of (-7 - 7i) + (6 - 4i)


#2:

Solutions:

$$a)\hspace{.1em}\frac{5\sqrt{2}}{2}+ \frac{5\sqrt{2}}{2}i$$

$$b)\hspace{.1em}{-\frac{3\sqrt{3}}{2}}- \frac{3}{2}i$$


#3:

Solutions:

$$a)\hspace{.1em}2\sqrt{3}(\text{cos}\hspace{.1em}135° + i \hspace{.1em}\text{sin}135°)$$

$$b)\hspace{.1em}4(\text{cos}\hspace{.1em}60° + i \hspace{.1em}\text{sin}60°)$$


#4:

Solutions:

$$a)\hspace{.1em}6(\text{cos}\hspace{.1em}150° + i \hspace{.1em}\text{sin}150°)$$

$$b)\hspace{.1em}3\left(\text{cos}\hspace{.1em}\frac{11π}{6}+ i \hspace{.1em}\text{sin}\frac{11π}{6}\right)$$


#5:

Solutions:

$$a)\hspace{.1em}\sqrt{21}\left(\text{cos}\hspace{.1em}\frac{2 π}{3}+ i \hspace{.1em}\text{sin}\frac{2 π}{3}\right)$$

$$b)\hspace{.1em}3\sqrt{2}(\text{cos}\hspace{.1em}225° + i \hspace{.1em}\text{sin}225°)$$