AnswersCUSD Advanced Math A 5.0Distance and Midpoints in the Complex Plane

Distance and Midpoints in the Complex Plane Answers

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1
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Compute .

Question illustration
A
Option
B
3
C
Option
2
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Compute .

Question illustration
A
Option
B
Option
C
Option
3

In general, what is the modulus of any complex number ?

Question illustration
A
Option
B
Option
C
Option
4

If the modulus is 4 and the real part is 2.0, what is the imaginary part?

A
0
B
3.5
C
7.2
5

If the modulus is 4 and the real part is –2.0, what is the imaginary part?

A
0
B
3.5
C
7.2
6

The set of all complex numbers with a given modulus (such as 5) always has the shape of a The modulus represents the of that shape.

A
line.
B
circle.
C
triangle.
D
square.
E
diameter
F
circumference
G
perimeter
H
radius
I
slope
7

How many complex numbers have a modulus of 5?

Answer:

infinite

8

The circle has a center at .

A
(3, 0)
B
(0, 3)
C
(0, 0)
9

Find the distance between the points below.4 + 3i and 9 – 9iDistance: units

Answer:

13

10

Find the midpoint of a segment with endpoints of 4 – 3i and –2 + 7i.

A
0.5i + 2i
B
1 + 2i
C
Option
D
Option
11

What mistake did Raul make?

A
He subtracted the values instead of adding them.
B
He did not add the corresponding parts of the complex numbers.
C
He found the sum instead of the average because he forgot to divide by two.
D
He added the numbers in the wrong order.
12

Find the center of the circle.

Answer:

3

13

Find the radius of the circle. units

Answer:

17

14

How many points have a modulus of 4?

A
2
B
4
C
infinitely many
15

If c + di is a point on the circle, then|c + di |= .

Answer:

3

16

How did you solve the problem? Check all of the boxes that apply.

A
I used the distance formula.
B
used the Pythagorean theorem.
C
I am comfortable using both the distance formula and the Pythagorean theorem because they are really the same idea.
D
Both methods are confusing; I am lost.

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