Representing complex numbers

Convert to polar form

• A

• B

• C

• D

Calculate the modulus (R) and argument (θ) for z = -5 + 3i

Give the argument between -π < θ < π.

• R = 5.83, θ = 0.54 rad or 31°

• R = 34, θ = 2.6 rad or 149°

• R = 5.83, θ = 3.7 rad or 211°

• R = 5.83, θ = 2.6 rad or 149°

Answer explanation

Find the trigonometric form of the complex number: z = √2 - √6i

• z = √8(cos(-60^o) + isin(-60^o))

• z = √8(cos(30^o) + isin(30^o))

• z = √8(cos(-120^o) + isin(-120^o))

• z = √8(cos(60^o) + isin(60^o))

Which of the following complex numbers is in polar form? Select all that apply.

• 5 + 3i

• 8 cis 44

• 10 cis 72

• -3 + 2i

4i

Write the complex number in trig form
 $r\left(\cos\theta+i\sin\theta\right)$  

• 4(cos 270 + i sin 270)

• 4 (cos 0 + i sin 0)

• 4 (cos 90 + i sin 90)

• 4 (cos 180 + i sin 180)

Covert the rectangular equation to polar form  $x^2+y^2=9$  

• r² = 81

• r = 3

• r = 4.5

• r sin θ = 9

10.1-10.2 Converting between rectangular and polar coordinates:
x = ?

• rcosθ
• rsinθ
• x² + y²
• y/x, x ≠ 0

Match the point in polar coordinates with either A, B, C, or D on the graph.
(2, 5π/6)

• A
• B
• C
• D