1. PROOF Prove

that if is a unit vector and is the angle between and then

2. PROOF Prove

that if is a unit vector and is the angle between and then

3. Geometrically,

the th roots of any complex number are all equally spaced around the unit

circle centered at the origin.

4. The product

of two complex numbers is zero only when the modulus of one (or both) of the

complex numbers is zero.

5. RIVER WIDTH A surveyor finds that a tree on the opposite bank of a river flowing

due east has a bearing of N E from a certain point and a bearing of N W from a

point 400 feet downstream. Find the width

1. PROOF Prove

that if is a unit vector and is the angle between and then

2. PROOF Prove

that if is a unit vector and is the angle between and then

3. Geometrically,

the th roots of any complex number are all equally spaced around the unit

circle centered at the origin.

4. The product

of two complex numbers is zero only when the modulus of one (or both) of the

complex numbers is zero.

5. RIVER WIDTH A surveyor finds that a tree on the opposite bank of a river flowing

due east has a bearing of N E from a certain point and a bearing of N W from a

point 400 feet downstream. Find the width of the river.

Q270;

1. GEOMETRY The lengths of the diagonals of a parallelogram are 10 feet and 16

feet. Find the lengths of the sides of the parallelogram if the diagonals intersect

at an angle of

2. GEOMETRY The lengths of the diagonals of a parallelogram are 30 meters and 40

meters. Find the lengths of the sides of the parallelogram if the diagonals intersect

at an angle.

3. NAVIGATION Two planes leave an airport at approximately the same time. One is

flying 425 miles per hour at a bearing of and the other is flying 530 miles per

hour at a bearing of Draw a figure that gives a visual representation of the

situation and determine the distance between the planes after they have flown

for 2 hours.

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