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