Complex Plane and Polar Form Summative Review

Find the absolute value of the complex number. Also state what quadrant the point would land in.

2 + 3i

• √13, Quadrant 1

• √5, Quadrant 1

• √11, Quadrant 2

• √11, Quadrant 3

Find the modulus of the complex number. Also state what quadrant the point would land in.

-3 + i

• √10, Quadrant 2

• √10, Quadrant 3

• 2, Quadrant 2

• 3, Quadrant 3

Express the given point in rectangular form.

4 ( cos π /3 + i sin π /3)

• 2 + 2√3 i

• 2 + √3 i

• 2 - 2√3 i

• -2 + 2√3 i

Write the complex number in polar form

 $5\ +\ 5i$  

• √50 (cos π/2 + i sin π/2)

• 50 (cos π/4 + i sin π/4)

• √50 (cos 5π/4 + i sin 5π/4)

• √50 (cos π/4 + i sin π/4)

Express the number given in trig form

 $3\ -\ 3i$  

•  $3\sqrt{2}\left(\cos\ \left(-45\degree\right)+i\sin\ \left(-45\degree\right)\right)$  

•  $3\left(\cos\ \frac{7\pi}{7}+i\sin\ \frac{7\pi}{4}\right)$  

•  $3\sqrt{2}\left(\cos\ \frac{7\pi}{4}+i\sin\ \frac{7\pi}{4}\right)$  

•  $3\sqrt{2}\left(\cos\ \frac{\pi}{4}+i\sin\ \frac{\pi}{4}\right)$  

Find the product of $z_1=3\left(\cos\ \frac{2\pi}{3}+i\sin\ \frac{2\pi}{3}\right)$  and

 $z_2=5\left(\cos\ \frac{\pi}{4}+i\sin\ \frac{\pi}{4}\right)$  

•  $15\left(\cos\ \frac{3\pi}{7}+i\sin\ \frac{3\pi}{7}\right)$  

•  $15\left(\cos\ \frac{\pi}{6}+i\sin\ \frac{\pi}{6}\right)$  

•  $15\left(\cos\ \frac{5\pi}{12}+i\sin\ \frac{5\pi}{12}\right)$  

•  $15\left(\cos\ \frac{11\pi}{12}+i\sin\ \frac{11\pi}{12}\right)$  

If a point is in Quadrant II, what do you need to add to the angle after calculating $Tan\ \theta$  

• add nothing

• add  $180\degree$  

• add  $270\degree$  

• add  $360\degree$  

If a point is located in Quadrant IV, how many degrees do I add after calculating $\tan\theta$  

• add nothing

• add $180\degree$  

• add  $270\degree$  

• add  $360\degree$  

Which complex point is graphed at point C in the complex plane shown?

• (-4, -1)

• -4 - i

• 4 + i

• -4 + i

Which complex point is graphed at point E in the complex plane shown?

• 3i

• -3i

• 3

• -3