1. PROOF Prove that if is a unit vector and is the angle between and then 2. PROOF Prove that if is.

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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