Complex Numbers Questions for Tests and Worksheets

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Grade 11 Complex Numbers

For each expression, select the most specific categorization possible.

	Real	Imaginary	Complex
$e^3 + pi$
$3i^2 + i$
$8i + 2i$
$-4^2$
$sqrt(-1) + sqrt(1)$
$(3i)^3$

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

Subtract the following complex numbers.

$(-2+4i) - (5-3i)$

$-7 + i$
$3 + 7i$
$-3 + i$
$-7 + 7i$

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

Factor.

$x^2+16$

$sqrt16i$
$(x-4i)(x+4i)$
$+-sqrt4$
$(x+2i)(x-2i)$

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

Simplify the complex number radical expression

$sqrt(-75)$ .

$-5sqrt3$
$5sqrt3$
$-5isqrt3$
$5isqrt3$

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

Perform the operation for the complex number radical expression

$sqrt(-64)+sqrt(-36)$ .

$-14i$
$14i$
$14$
$-14$

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

The complex number

$2-5i$ is in which quadrant?

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

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

Add the following complex numbers.

$(3+4i) + (-1+3i)$

$2 + 7i$
$4 + 7i$
$-15 + 5i$
$2 + i$

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

Write

$(3 + 2i) - (4 - 3i)$ in standard form.

$- 1 +5i$
$-1 - i$
$7 - i$
$7 + 5i$

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

Find the distance between

$z = 6 + 7i$ and

$w = -2 - 3i$ in the complex plane.

$4sqrt(2)$
$18$
$2sqrt(2)$
$2sqrt(41)$

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

André is working on a math problem where he has to subtract two complex numbers graphically. They are

$z_1 = 3-8i$ and

$z_2 = -5+i$ . If he is using the translation method, and is subtracting

$z_1$ from

$z_2$ , which complex number is considered the starting point, and then how is it translated?

$z_1$ is the starting point, and is translated 5 units left and 1 unit up.
$z_1$ is the starting point, and is translated 5 units right and 1 unit down.
$z_2$ is the starting point, and is translated 3 units right and 8 units down.
$z_2$ is the starting point, and is translated 3 units left and 8 units up.

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

Simplify the complex number radical expression

$sqrt(-96)$ .

$-4isqrt6$
$4sqrt6$
$4isqrt6$
$-4sqrt6$

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

Simplify the complex number expression

$-25i^25$ .

$-25$
$25$
$25i$
$-25i$

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

Multiply and simplify the complex numbers in the following expression.

$(-3+2i)(-6-8i)$

$-34-12i$
$34+12i$
$34-12i$
$-34+12i$

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

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

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

$-7i$
$2 + 3i$
$-3i + 2$
$2 - 3i$

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

Factor.

$x^2+12$

$2sqrt3i$
$(x-4i)(x+4i)$
$+-sqrt12$
$(x+2sqrt3i)(x-2sqrt3i)$

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

What is the distance between the complex numbers

$2-4i$ and

$-3/2 - 1/2 i$ in the complex plane?

$7/2 sqrt(2)$
$1/2sqrt(130)$
$5/2 sqrt(2)$
$1/8 sqrt(82)$

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

Find the product.

$(7 - 6i)(-8 + 3i)$

$-56 + 18i$
$-56 - 18i$
$-38 + 69i$
$-38 - 69i$
$29 + 11i$
$-29 + 11i$

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

Which of the following is the factored form of

$x^3 + 8$ over the complex numbers?

$(x+2)(x-1+sqrt(3) \ i)(x-1-sqrt(3) \ i)$
$(x+2)(x-2)(x+2)$
$(x+2)(x-2i)(x+2i)$
$(x+2)(x+2+2sqrt(3) \ i)(x-2-2sqrt(3) \ i)$

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

Simplify the complex number radical expression

$sqrt(-350)$ .

$-5sqrt14$
$-5isqrt14$
$5isqrt14$
$5sqrt14$

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

Subtract.

$(-3 + 2i) - (-4 - 8i)$

$-7 - 6i$
$1 + 10i$
$1 - 6i$
$7+ 10i$

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