CH 6 PRECALC TEST

Find the quotient z1z2 of the complex numbers: z1 =24(cos⁡ 300∘ + i sin⁡ 300∘) and z2 =8(cos⁡ 75∘ + i sin ⁡75∘).

(-3√2)/2 - (3√2)/2 i

Let u be the vector with initial point (2,−5) and terminal point (−1,3). Write u as a linear combination of the standard unit vectors i and j.

-3i+8j

Find the one cube roots of z= -2+2i

1+i

Find magnitude of the vector v that has initial point (4,−7)and terminal point (−1,5)

13

Find the product z1z2 of the complex numbers: z1 = 2(cos⁡(2π/3) + i sin⁡(2π/3)) and z2 = 8(cos⁡(11π/6) + i sin⁡(11π/6))

16i

Find the angle between u= <4,3> and v= <3,5>

22.2°

Find dot product <4,5> ⋅ <2,3>

23

A force of 600 pounds is required to pull a boat and trailer up a ramp inclined at 15∘ from the horizontal. Find the combined weight of the boat and trailer.

2318

To close a barn's sliding door, a person pulls on a rope with a constant force of 50 pounds at a constant angle of 60∘. Find the work done in moving the door 12 feet to its closed position.

300 foot-pound

Write the complex number z= -2-2 √3i in trigonometric form.

4(cos(4π/3) + i sin (4π/3))

Use DeMoivre's Theorem to find (-1+√3i)¹²

4096

Find the direction angle of vector v= 3i-4j.

53.13

Find a unit vector in the direction of v= <-2,5>

<-2√29/29, 5√29/29>

Find the component form of the vector v that has initial point (4,−7) and terminal point (−1,5).

<-5,12>

Find the component form of the vector that represents the velocity of an airplane descending at a speed of 100 miles per hour at an angle of 30∘ below the horizontal.

<-50√3,-50>

Let u= <-1,3> , v= <2,4> , w= <1,-2> . Find dot product (u⋅v)w

<10,-20>

Are the vectors u= <2,−3>and v= <6,4> orthogonal?

orthogonal

Write the complex number z= √8⌈cos⁡(−π/3) + i sin⁡(−π/3)⌉ in standard form.

√2-√6i

Find the absolute value z= -2+5i

√29

The dot product of u with itself is 5. What is the magnitude of u?

√5