Reviewing Complex Numbers and Solutions of Quadratics

• 0 real solutions

• 1 real solution

• 2 real solutions

Answer explanation

Expand the right side of the equation by squaring (x+3). Then use algebraic methods to solve for x. If the solution involves the square root of a negative number, then the equation has no real solution.

Tags

CCSS.HSA.REI.B.4

How many real solutions are there for the system of equations graphed on the coordinate plane?

• 0 real solutions

• 1 real solution

• 2 real solutions

• 3 real solutions

Answer explanation

Remember that a solution is characterized by a point of intersection. Count the number of points of intersection to determine the number of real solutions.

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Complex numbers include which two subsets?

Select two correct answers.

• real

• imaginary

• rational

• irrational

Answer explanation

Real numbers are comprised of rational and irrational numbers.

On the other hand, a complex number is in the form of "a+bi" where "a" is the real part and "bi" is the imaginary part.

Tags

CCSS.HSN.CN.A.1

• integer

• rational

• imaginary

• complex

Answer explanation

The number "a+bi" is a complex number.

The "a" is the real part of the complex number.

What does the "i" represent?

Tags

CCSS.HSN.CN.A.1

Answer explanation

Isolate the squared term. The linear terms will cancel. Then take the square root of both sides to solve for x. Finally, simplify any square roots, remembering the square root of any negative number involves "i".

Tags

CCSS.HSA.REI.B.4

Answer explanation

Recall that a complex number is a number in the form a+bi, where "a" is the real part, and "b" is the imaginary part.

The real part is 8.4.

Simplify the radical expression as an imaginary number.

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

• Commutative Property of Addition

• Associative Property of Multiplication

• Distributive Property

• None of these

Answer explanation

The distributive property allows us to take a number outside of the parentheses and multiply it by both the real and imaginary part of a complex number.

Commutative Property: m + n = m + n

Associative Property: (mn)*p = m*(np)

Tags

CCSS.HSN.CN.A.2

Answer explanation

Be sure to combine like terms inside the [brackets] before distributing.

Then distribute the "5i" to both terms in the bracket.

What does i² equal?

Tags

CCSS.HSN.CN.A.2

Answer explanation

Each negative radicand can be rewritten as an imaginary number.

√-25 can be rewritten as 5i

√-9 can be rewritten as 3i

Finally, simplify: 5i + 4i + 11 - 3i

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

CCSS.HSN.CN.B.4

CCSS.HSN.RN.A.2

Answer explanation

First apply the Distributive Property to both terms in the second set of parentheses.

(9.3 - 2.4i) - (-1.4 + 3.8i)

9.3 - 2.4i + 1.4 - 3.8i

Then combine the real parts and the imaginary parts.

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2