Vectors and Their Components Answers

What is the modulus and argument after gets raised to the 6th power?

What is the additive identity of the complex number 14 + 5i?

Review the proof of de Moivre’s theorem (not in order). Proof of de Moivre's Theorem [cos(θ) + i sin(θ)]k + 1A= [cos(θ) + i sin(θ)]k ∙ [cos(θ) + i sin(θ)]1B= cos(kθ + θ) + i sin(kθ + θ)C= cos(kθ)cos(θ) − sin(kθ)sin(θ) + i [sin(kθ)cos(θ) + cos(kθ)sin(θ)]D= [cos(kθ) + i sin(kθ)] ∙ [cos(θ) + i sin(θ)]E= cos[(k + 1)θ] + i sin[(k + 1)θ]

Which values of p and q would make the value of the following expression equal to 58i? (3 – 7i)(p + qi)i

Consider the limaçon with equation r = 3 + 4cos(θ). How does the quotient of a and b relate to the existence of an inner loop?

Review the graph of complex number z.

Which equation represents the rectangular form of r = 4cos(θ)?

For the complex number ,what is the polar form?

Which graph represents points on the polar curve r = 2 + 5sin(θ)?

Which pair of complex numbers has a real-number product?

In a video game, two objects move around the screen according to the equations r = 4cos(θ) and r = –1 + 2cos(θ). Which coordinates represent a possible collision point of the objects?

Which expression represents a 5th root of –i?

What is the value of ?

Review the graph.

Review the four points shown on the polar coordinate system.

In the complex plane, the rectangular coordinates (x, y) represent a complex number. Which statement explains why polar coordinates (r, θ) represent the same complex number?

Which equation represents the polar form of x2 + (y + 4)2 = 16?

Which of the following is a square root of ?

Review the graph.

Which graph represents the polar curve r = 4sin(θ)?