Answers Summer_Advanced AlgebraDistance and Midpoints in the Complex Plane

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The following statements concern the modulus. Which statement is false?

The modulus represents the distance between the complex number and the origin.

The algorithm to find the modulus is based on the Pythagorean theorem.

The modulus is sometimes negative because of the computations with i.

The modulus is an extension of the absolute value in the complex plane.

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Which statements about the function are true? Select three options.

The vertex of the function is at (–4,–15).

The vertex of the function is at (–3,–16).

The graph is increasing on the interval x > –3.

The graph is positive only on the intervals where x < –7 and wherex > 1.

The graph is negative on the interval x < –4.

An isosceles triangle’s altitude will bisect its base. Which expression could be used to find the area of the isosceles triangle above?

StartFraction start root 40 end root . start root 40 end root over 2 EndFraction

StartFraction start root 40 end root . start root 68 end root over 2 EndFraction

StartFraction start root 232 end root . start root 288 end root over 2 EndFraction

StartFraction start root 232 end root . start root 164 end root over 2 EndFraction

What is the greatest possible integer value of x for which is an imaginary number?

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 15 EndRoot Over 11 EndFraction

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction 2 StartRoot 15 EndRoot Over 11 EndFraction

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot Over 11 EndFraction

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot i Over 11 EndFraction

Which equation is an example of the commutative property of multiplication?

(4 + 2i) = (2i + 4)

(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)

(4 + 2i)(3 – 5i) = (4 + 2i)(3 – 5i)(1)

(4 + 2i) = (4 + 2i + 0)

What is the y-value of the vertex of the function f(x)=−(x+8)(x−14)?

112

121

A point of the form 25 +bi is 37 units from 13 – 31i. What is the value of b?

6.6

36.6

40.6

The following statements are about finding a midpoint of a segment in the complex plane. Which statement is false?

The midpoint is the average of the endpoints.

First add the endpoints and then multiply by 1/2.

First subtract the endpoints and then divide by 2.

The midpoint of complex conjugates will lie on the x-axis.

If the discriminant of a quadratic equation is 4, which statement describes the roots?

There are two complex roots.

There are two real roots.

There is one real root.

There is one complex root.

Which point shows the location of 5 – 2i on the complex plane below?

point A

point B

point C

point D

What is the sum of 12 – 5i and –3 + 4i?

–16 + 63i

9 – i

9 – 9i

15 – 9i

Solve for in the equation .

x = 3 plus-or-minus StartRoot 23 EndRoot

x = 3 plus-or-minus StartRoot 51 EndRoot

x = 3 plus-or-minus StartRoot 41 EndRoot

x = 3 plus-or-minus StartRoot 5 EndRoot

What are the values of x in the equation x2 – 6x + 9 = 25?

x = –2 or x = 8

x = –1 or x = –11

x = 1 or x = 11

x = 2 or x = –8

Which pair of complex numbers has a real-number product?

(1 + 3i)(6i)

(1 + 3i)(2 – 3i)

(1 + 3i)(1 – 3i)

(1 + 3i)(3i)

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