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Complex Numbers Questions - All Grades

You can create printable tests and worksheets from these Complex Numbers questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

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

Multiply and solve the following complex number expression.

$(-16+30i)^2$

$-644+960i$
$644+960i$
$-644-960i$
$644-960i$

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

Find the product.

$4i(2 - 8i)$

$4i$
$0$
$-32 + 8i$
$32 + 8i$
$-4i$

Grade 11 Complex Numbers CCSS: HSN-CN.B.4

The complex number

$5+7i$ is in which quadrant?

$I$
$II$
$III$
$IV$

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

Simplify the complex number radical expression

$sqrt(-160)$ .

$-4isqrt10$
$-4sqrt10$
$4isqrt10$
$4sqrt10$

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

Add.

$(5-2i) + 3i$

$11$
$6 + 15i$
$5 + i$
$5 - 5i$

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

$z = 5 + 4i$ , and is plotted in the complex plane, which of the following complex numbers would be 3 units away from

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

$2 + 4i$
$6 + 6i$
$3 + (4+sqrt(5)) \ i$
$8 + i$

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

Let

$z=-8+5i$ . If the midpoint of the line segment created by complex numbers

$z$ and

$w$ is

$-3+3/2 i$ , what is the value of

$w ?$

$w = -11/2 + 13/4 i$
$w = 2-2i$
$w = 14 + i$
$w = 4 + 7/2 i$

Grade 11 Complex Numbers

Factor the polynomial

$4x^2+49$ . An imaginary number in the answer is possible.

$(2x-7)(2x+7)$
$(2x+7i)(2x-7i)$
$(2x-7i)(2x-7i)$
$(2x+7i)(2x+7i)$

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

Simplify the complex number radical expression

$sqrt(-1000)$ .

$10isqrt10$
$-10isqrt10$
$10sqrt10$
$-10sqrt10$

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

Evaluate fully.

$(8-3i)(3+2i)$

$30-7i$
$18-25i$
$-6i^2+7i+24$
$30+7i$

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

Divide and simplify the complex number expression.

$-5/(-5i)$

$-i$
$i$
$i^3$
$-i^3$

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

What does

$i^45$ equal?

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

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

Simplify the complex number radical expression

$sqrt {:-1600$ .

$-40$
$40$
$-40i$
$40i$

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

What is the complex conjugate of

$3 + 4i ?$

$-3 - 4i$
$-3+4i$
$4i + 3$
$3-4i$

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

$z= -11 + 2i$ and

$w= -1 + 6i$ are plotted on the complex plane, and a line segment created by joining the two points, what would be the midpoint of this line segment?

$-5 - 2i$
$-5/2 + 5/2i$
$-6 + 4i$
$-6 + 3i$

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

For the polynomial

$P(x) = (ax)^3 + b^3$ ,

$a,b in RR$ , and where

$a,b$ are positive, if

$1 + sqrt(3)i$ is a root, and in fully factored form there is a leading constant of 8, what are the coefficients

$a,b ?$ (Assume that the coefficient of 8 has come from factoring out a 2 from each of the three factors of

$P(x)$ ).

$a=1, b=2$
$a=1, b=4$
$a=2, b=4$
Not enough information to solve.

Grade 11 Complex Numbers CCSS: HSN-CN.B.4

What is the rectangular form of the complex number whose polar coordinates are

$(6, -18°) ?$

$5.7 - 0.3 i$
$5.7 - 1.9i$
$5.7 + 1.9i$
$1.9 - 5.7i$

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

Evaluate.

$(4i)/(7-3i)$

$20/29 i$
$-3/10 + 7/10 i$
$1/7 - 4/3 i$
$-6/29 + 14/29 i$

Grade 10 Complex Numbers CCSS: HSN-CN.A.2

$i^2=-1$ , then what is the value of

$i^32$ ?

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

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

Evaluate.

$3i + (-4+2i)$

$-4+5i$
$4+5i$
$-4+i$
$4+i$

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Complex Numbers Questions - All Grades