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Complex Numbers Questions - All Grades

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Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Find the quotient. 8i-1+3i
  1. 12-4i5
  2. -12+4i-5
  3. -1+8i3
  4. 1+8i-3
  5. 5i
  6. -5i
Grade 12 Complex Numbers
a + bi is an example of                   of complex numbers.
  1. trig form
  2. polar form
  3. rectangular form
  4. none of the above
Grade 11 Complex Numbers CCSS: HSN-CN.A.1
What is √800+√-50 ?
  1. 20√2+25i
  2. √800+50i
  3. 20√2+5i√2
  4. 25i√2
Grade 11 Complex Numbers CCSS: HSN-CN.C.8
Which of the following are equivalent to x4-16? Choose all that apply.
  1. (x+2)(x3-2i x2-4x+8i)
  2. (x+2)(x-2)(x+2i)(x-2i)
  3. (x+2)(x-2)(x2+4)
  4. (x+2i)(x-2i)(x2-4)
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Perform the indicated operation.
(3-5i)-(-3+4i)
  1. i
  2. 6-9i
  3. 6-i
  4. -9i
Grade 11 Complex Numbers CCSS: HSN-CN.C.8
Factor the quadratic expression x2+81.
  1. (x+9i)(x-9i)
  2. (x+9i)(x+9i)
  3. (x-9i)(x-9i)
  4. (x+9i2)(x+9i2)
Grade 11 Complex Numbers CCSS: HSN-CN.B.5
If z=-2+7i is plotted in the complex plane, how can multiplying by -1 be described geometrically? Choose all correct answers.
  1. It rotates z 90° clockwise about the origin.
  2. It rotates z clockwise 180° about the origin.
  3. It reflects z across the imaginary and real axis.
  4. It reflects z across the real axis.
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
Convert 3√7 (cos80°+isin80°) to rectangular form.
  1. 7.8+1.4i
  2. 1.4+1.0i
  3. 1.4+7.8i
  4. 0.2+1.0i
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
Convert -4+2i to polar form.
  1. 2√5 [ cos(153.4°)+isin(153.4°) ]
  2. 2√3 [ cos(153.4°)+isin(153.4°) ]
  3. 2√5 [ cos(-26.6°)+isin(-26.6°) ]
  4. 2√3 [ cos(-26.6°)+isin(-26.6°) ]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Given z=8-2i, find |z|.
  1. 2√17
  2. 2√15
  3. 68
  4. 60
Grade 12 Complex Numbers CCSS: HSN-CN.C.8
Find the roots of x2+12.
  1. 2√3
  2. ±2√3i
  3. ±√12
  4. (x+2√3i)(x-2√3i)
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Evaluate the complex expression i1400.
  1. -1
  2. 1
  3. √-1
  4. -i
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Multiply 5-12i by its conjugate.
  1. 169i
  2. 169
  3. 25+34i+144i2
  4. 203i3
Grade 11 Complex Numbers
What is the real part of 2+4i?
  1. 4
  2. 4i
  3. 2
  4. 2i
Grade 11 Complex Numbers CCSS: HSN-CN.C.8
Factor the quadratic expression x2+25.
  1. (x+5i)(x+5i)
  2. (x+5i)(x-5i)
  3. (x-5i)(x-5i)
  4. (x+5i2)(x-5i2)
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
What is the complex conjugate of -250+81i?
  1. -250-81i
  2. 250-81i
  3. -250+81i
  4. 250+81i
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Expand and simplify. (10-12i)(10+12i)
  1. 100-144i
  2. 244
  3. 244i2
  4. 244i
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Divide and simplify the following complex number expression. 4-9i-6i
  1. -32+23i
  2. 32+23i
  3. -32-23i
  4. 33-23i
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
What is the complex conjugate of -7+15i?
  1. -7-15i
  2. -7+15i
  3. 7-15i
  4. 7+15i
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