6.6.5 - Test (CST): Complex Numbers Precalculus Sem 2

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Which of the following are correct statements concerning the roots of unity? Check all that apply

1 is always the nth root of unity nth roots of unity are evenly spaced on the unit circle. https://ibb.co/ky3iTz (Answer)

Calculate |-5 + 12i|.

13 https://ibb.co/gTztve (Answer)

Convert the complex number 3-3i into its polar representation.

3sqrt2(cos(315 degrees) + i sin(315 degrees)) https://ibb.co/mNgqae (Answer)

Simplify (-1-3i)+2(4+6i) Enter your answer in the form a+bi.

7+9i https://ibb.co/hcKkae (Answer)

What is the name of the shape graphed by the function r=1 + sin theta?

Cardioid https://ibb.co/eTSA8z ( Answer)

The value of theta represents the distance from a point to the origin when plotting a point in polar coordinates.

False https://ibb.co/ix1Z1K (Answer)

What is the name of the shape graphed by the function r^2 =4cos theta?

Lemniscate https://ibb.co/gWf2MK ( Answer)

What is the name of the shape depicted in the graph below? https://ibb.co/eEg6Fe (Imagen)

Lemniscate https://ibb.co/gYaNoz (Answer)

What is the name of the shape graphed by the function theta = 5pi/3 ?

Line https://ibb.co/jFb6Fe (Answer)

What is true about the complex number -5 + 5i? Check all that apply.

The modulus is 5sqrt2 It lies in quadrant 2 https://ibb.co/nkDmFe (Answer)

A rectangular equation that is not a function may be a function in the polar coordinate system.

True https://ibb.co/hum91K ( Answer)

Fin the product of the complex numbers. Express your answer in trigonometric form. Z1=7(cos15degrees)+isin(15degrees)) Z2=2(cos110degrees)+isin(1110degrees))

Z1=14(cos125degrees)+isin(125degrees) https://ibb.co/mc7Dve (Answer)

When a complex number z is written in its polar from, z = r(cos theta + i sin theta), the non-negative number r is called the ______ of z.

modulus https://ibb.co/ionwFe (Answer)

An equation whose variables are polar coordinates is called a ______.

polar equation https://ibb.co/jyoNMK (Answer)

In polar coordinates, the origin is called the _____.

pole https://ibb.co/hQ16Fe (Answer)

Convert (5, (pi/4)) to rectangular coordinates.

((5sqrt2)/2), ((5sqrt2)/2)) https://ibb.co/iWQNoz (Answer)

Convert 4(cos(120 degrees) + i sin (120 degrees)) into rectangular form.

(-2,2sqrt3) https://ibb.co/cWSMFe (Answer)

Which set of polar coordinates name the same point as (5, pi/4)?

(-5, 5pi/4) https://ibb.co/dFEF8z (Answer)

Convert the polar representation of this complex number into its standard form. 2(cos(7pi/6)+isin(7pi/6))

-sqrt3 -i https://ibb.co/kzf8ve ( Answer)

Use de Moivre's theorem to write the complex number in trigonometric form. (cos(pi/4)+i sin(pi/4))^3

cos(3pi/4)+isin(3pi/4) https://ibb.co/g0rgFe (Answer)


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