Complex Numbers Questions for Tests and Worksheets

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Grade 12 Complex Numbers CCSS: HSN-CN.C.8

Factor.

$x^2+64$

$(x+8i)(x-8i)$
$(x-8)(x+8)$
$+-sqrt64$
$(x+64i)(x-64i)$

Grade 11 Complex Numbers CCSS: HSN-CN.A.2

Solve.

$(14+6i)(14-6i) =$

$232i$
$-232i$
$232$
$-232$

Grade 11 Complex Numbers CCSS: HSN-CN.C.8

Factor quadratic expression

$x^2 + 121$ .

$(x-11i)(x-11i)$
$(x+11i)(x-11i)$
$(x+11i)(x+11i)$
$(x+11i^2)(x-11i^2)$

Grade 11 Complex Numbers CCSS: HSN-CN.A.3

Simplify.

$(2-i)/(-3+6i)$

$-4/9-1/3i$
$-4/15-1/3i$
$-4/15-1/5i$
$-1/5i$

Grade 11 Complex Numbers CCSS: HSN-CN.A.2

Find the product.

$5i(-i)$

$-5$
$5$
$-5i$
$5i$
$1$

Grade 11 Complex Numbers

Which expression does NOT have a real number value?

$root3(-8)$
$sqrt(-4)$
$sqrt(3)$
$root3( 10)$

Grade 11 Complex Numbers CCSS: HSN-CN.A.2

Add or Subtract the complex number expression:

$(12+8i)-(11-4i)$ .
This is not the FOIL method. Write your answer in the correct complex number form.
1+12i

Grade 11 Complex Numbers CCSS: HSN-CN.A.3

Multiply

$6+5i$ by its conjugate.

$61$
$61i$
$36+22i+25i^2$
$82i^3$

Grade 11 Complex Numbers CCSS: HSN-CN.B.5

$z = -4+2i$ is plotted in the complex plane, how can multiplying by

$i$ be described geometrically?

It rotates $z$ 90° counterclockwise about the origin.
It rotates $z$ 90° clockwise about the origin.
It reflects $z$ across the imaginary axis.
There is no geometric interpretation.

Grade 11 Complex Numbers CCSS: HSN-CN.B.5

Let x represent the real axis and y the imaginary axis in the graph below. Given the complex number

$2+4i$ , represented by C, which of the following represents its conjugate?

H
D
B
Its conjugate is not represented by any given value on this graph.

Grade 11 Complex Numbers CCSS: HSN-CN.A.1

Which of the following is the correct simplified form of the expression

$-sqrt(-4) - sqrt(9) ?$

$-5i$
$-3-2i$
$3-2i$
$2i-3$

Grade 11 Complex Numbers CCSS: HSN-CN.A.2

Simplify:

$8i^6+6i^5-5i^3-3i^2-7i-9$

$-14+4i$
$-4+4i$
$-10i$
$-14-18i$

Grade 10 Complex Numbers CCSS: HSN-CN.A.3

Simplify.

$(1+2i)/ (2-3i)$

$(8/7) + i$
$(8/7) + (1/7)i$
$-4+7i$
$-(4/13) +(7/13) i$

Grade 11 Complex Numbers CCSS: HSN-CN.A.2

Multiply and write the result in standard form.

$4i(3i - 2)$

$-12i-8$
$12+8i$
$-12-8i$
$12i+8$

Grade 11 Complex Numbers CCSS: HSN-CN.B.6

Which of the following expressions represent(s) the distance between

$z_1$ and

$z_2$ in the complex plane? Choose all correct answers.

$|z_1 - z_2|$
$|z_2 - z_1|$
$|z_2| - |z_1|$
$|z_2 + z_1|$

Grade 11 Complex Numbers CCSS: HSN-CN.B.6

Let the graph below represent the complex plane, where x is the real axis and y is the imaginary axis. What is the midpoint of the line segment created by joining the two complex numbers represented by J and C?

$1/2 + 5/2 i$
$3/2 + 3/2 i$
$-3/2 -3/2 i$
$1 + 5i$

Grade 11 Complex Numbers CCSS: HSN-CN.A.2

Simplify the imaginary unit in the following expression.

$i^25+i^17$

$sqrt(-1)$
$2i$
$-2i$
$-1$

Grade 11 Complex Numbers CCSS: HSN-CN.B.5

One method for adding or subtracting complex numbers in the complex plane is to look at the numbers as vectors, and then add or subtract these vectors as is done with vectors in the real plane. A vector is defined as something having both a direction and a magnitude. Why can complex numbers in the complex plane be represented as vectors? Choose all correct answers.

They can't really, but it's a useful tool to use when adding or subtracting.
Because, as seen in polar form, they have a magnitude, $r$ , and direction, $theta$ .
Because they are represented by two "coordinates", a real and imaginary value, which is similar to the component form of a vector.
Because complex numbers and vectors are identical.

Grade 11 Complex Numbers CCSS: HSN-CN.A.2

Subtract.

$(8 + 4i) - 6i$

$8 + 2i$
$8 - 2i$
$-8-2i$
$8 + 10i$

Grade 11 Complex Numbers CCSS: HSN-CN.A.1

To write a complex number in standard form, the real number part proceeds the imaginary number part.

True
False

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