The Complex Number System - CCSS Practice

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This quiz illustrates the range of difficulty expected by the following Common Core State (CCS) standards:

QuestionCommon Core Standard #
1N.CN.1
2N.CN.1
3 N.CN.2
4N.CN.2
5N.CN.2
6N.CN.3 +
7N.CN.3 +
8N.CN.5 +
9N.CN.5 +
10N.CN.6 +
11N.CN.7
12N.CN.8 +
indicates a modeling standard.
+ indicates a college and career ready standard.

All questions of this quiz illustrate the difficulty of the high school N.CN standards required for all students, including the college and career ready students.



Question 1: Rewrite the complex number z = ai3 + bi2 + ai + b in standard form.












Question 2: Rewrite the complex number



in a standard form z = a + bi.











Question 3: Calculate z = z1 + z2:

z1 = 3i2 - 2i + 1
z2 = -i2 - i + 5











Question 4: Calculate and write z = z1 - z2 in a standard form z = a + bi.

z1 = i2 - i + 2
z2 = -2i2 + 3i + 3

z =


Question 5: Calculate and write z = z1 × z2 in a standard form z = a + bi.

z1 = i + 2
z2 = -i + 3

z =



Question 6: Calculate the modulus of the complex number z = -3 + 4i

|z| =



Question 7: Simplify the complex number:













Questions 8 and 9:


The modulus of z is and its argument is o.



Questions 10: The length of the line segment between 6-3i and 1+9i in the complex plane is .


Question 11: The solutions of the quadratic equation x2 - 4x + 5 = 0 are:












Question 12: x2 + 36 =












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