Converting Complex Numbers to Polar Form

Write the complex number in polar form

• √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)

Write the complex number in polar form

• 3 ( cos 3π/2 + i sin 3π/2)

• 3 ( cos π/2 + i sin π/2)

• 9 ( cos 3π/2 + i sin 3π/2)

• 3 ( cos 2π + i 2π)

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

Identify the rectangular form, modulus, and argument of the complex number represented on the graph.

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

Write the complex number in trig form r(cosθ+i sinθ)

• 4(cos 270 + i sin 270)

• 4 (cos 0 + i sin 0)

• 4 (cos 90 + i sin 90)

• 4 (cos 180 + i sin 180)

Find    
5(cos 2π /3 + i sin 2π /3)⋅2( cos π /3 + i sin π /3)
in polar form.  Then express your final answer in rectangular form.

• -10

• 10

• -10i

• 10i