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Complex Numbers Questions - All Grades

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Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Add the complex numbers. [math](-3+7i) + (3 - i)[/math]
  1. [math]6i[/math]
  2. [math]6 + 8i[/math]
  3. [math]-6 + 6i[/math]
  4. [math]6 + 6i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Subtract the complex numbers. [math]3i - (-5 + 3i)[/math]
  1. [math]5[/math]
  2. [math]-5 - 6i[/math]
  3. [math]5 + 6i[/math]
  4. [math]-5[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Write the expression as a complex number in standard form.

[math](3 - 5i)(1 + 3i)[/math]
  1. [math]3 - 15i[/math]
  2. [math]-2i + 4i[/math]
  3. [math]18 + 4i[/math]
  4. [math]15 - 2i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Evaluate. [math](5 - 6i) - (-3 + 9i)[/math]
  1. [math]2 + 3i[/math]
  2. [math]2 - 3i[/math]
  3. [math]8 - 15i[/math]
  4. [math]8 + 3i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Divide the complex numbers. [math](-13+i) / (4+4i[/math]
  1. [math]"Undefined"[/math]
  2. [math]-13/4 + 1/4 i[/math]
  3. [math]- 3/2 + 7/4 i[/math]
  4. [math] -7/4 + 7/4 i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Multiply the complex numbers. Leave in the form [math]a+bi[/math].

[math](8 - 2i) (3i)[/math]
  1. [math]24 - 6i[/math]
  2. [math]-6 + 24i[/math]
  3. [math]6 + 24i[/math]
  4. [math]24 + 6i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Divide the complex numbers. [math](8-8i) / (2-2i)[/math]
  1. [math]"Undefined"[/math]
  2. [math]0[/math]
  3. [math]4[/math]
  4. [math]4-4i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Divide the complex numbers.

[math](3 + 2i)/(8 - i)[/math]
  1. [math]22/65 + 19/65 i[/math]
  2. [math]3/8 - 2i[/math]
  3. [math]22/63 + 9/63 i[/math]
  4. [math]-13/8[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Evaluate. [math](9-3i) / (-6-3i)[/math]
  1. [math]0[/math]
  2. [math]-1+i[/math]
  3. [math]1-i[/math]
  4. [math]-5/3 + 5/3 i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Add. [math](3-9i) + 4i[/math]
  1. [math]7-9i[/math]
  2. [math]3+13i[/math]
  3. [math]3-5i[/math]
  4. [math]3-13i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Evaluate. [math](4 + 2i) / (1-2i)[/math]
  1. [math]4-i[/math]
  2. [math]2i[/math]
  3. [math]3[/math]
  4. [math]-(10i)/3[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
What is the polar form of the complex number [math]-5 ?[/math]
  1. [math] -5 \ (cos180° + i sin180°)[/math]
  2. [math]5 \ (cos0° + i sin0°)[/math]
  3. [math]5 \ (cos180° + isin180°)[/math]
  4. [math]"This is not a complex number."[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Find the sum of the complex numbers. [math]i + 6i[/math]
  1. [math]6i[/math]
  2. [math]-6[/math]
  3. [math]5i[/math]
  4. [math]5[/math]
  5. [math]7i[/math]
  6. [math]-7[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Evaluate. [math]3/(6i)[/math]
  1. [math]1/2 i[/math]
  2. [math]1+1/2 i[/math]
  3. [math]-1/2[/math]
  4. [math]-1/2 i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.C.8
Factor [math]x^4-1[/math].
  1. [math](x^2+1)(x+1)(x+i)[/math]
  2. [math](x+1)(x-1)(x+1+i)(x-1-i)[/math]
  3. [math](x+1)(x-1)(x+i)(x-i)[/math]
  4. [math](x+1)(x-1)(x+sqrt(2)i)(x-sqrt(2)i)[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Multiply and simplify the complex numbers. [math]-6i(70-85i)[/math]
  1. [math]510+420i[/math]
  2. [math]510-420i[/math]
  3. [math]-510+420i[/math]
  4. [math]-510-420i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Divide. [math](4i) / (12i)[/math]
  1. [math]1/3[/math]
  2. [math] -1/3 i[/math]
  3. [math]-1/3[/math]
  4. [math]1-1/3i[/math]
Grade 11 Complex Numbers
For each expression, select the most specific categorization possible.
Real Imaginary Complex
[math]e^3 + pi[/math]
[math]3i^2 + i[/math]
[math]8i + 2i[/math]
[math]-4^2[/math]
[math]sqrt(-1) + sqrt(1)[/math]
[math](3i)^3[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.C.8
If [math]x - 3/2 + 3/2sqrt(3) \ i[/math] is a factor of [math]x^3 + 27[/math], which of the following are also factors of this polynomial?
  1. [math]x - 3[/math]
  2. [math]x + 3/2 - 3/2 sqrt(3)[/math]
  3. [math]x - 3/2 - 3/2 sqrt(3) \ i [/math]
  4. [math]x + 3/2 - 3/2 sqrt(3) \ i[/math]
Grade 10 Complex Numbers CCSS: HSN-CN.A.2
Simplify problem to discover product of [math](2 - i)(4 + 5i)[/math] in standard form.
  1. [math]13 - 6i[/math]
  2. [math]8 + i[/math]
  3. [math]3 + 6i[/math]
  4. [math]13 + 6i[/math]
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