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Back to Tutor Intake Assessment: The Complex Number System

HSN.CN Tutor Intake -- Complex Numbers

This short check helps your tutor understand where to start with complex
numbers. Answer each question on your own without notes or a calculator.
If you are unsure, give your best try — the goal is to find what to work
on together, not to grade you.

Grade 10·12 problems·~14 min·Common Core Math - HS Number and Quantity·domain·cn
Work through problems with immediate feedback
A

Concepts

1

The imaginary unit ii is defined so that i2=−1i^2 = -1. Which
statement correctly explains why ii is defined this way?

2

A complex number is written in standard form a+bia + bi, where
aa and bb are real numbers. For the complex number −5+3i-5 + 3i,
which statement is correct?

3

A student computes the discriminant of x2+4x+13=0x^2 + 4x + 13 = 0
and gets b2−4ac=16−52=−36b^2 - 4ac = 16 - 52 = -36. What does this tell
us about the solutions?

B

Procedures

1

Using the pattern i1=ii^1 = i, i2=−1i^2 = -1, i3=−ii^3 = -i, i4=1i^4 = 1
(cycle of length 4), what is i23i^{23}?

2

Compute (3+5i)−(7−2i)(3 + 5i) - (7 - 2i) and write the result in the form
a+bia + bi. Enter the real part aa and then the imaginary part bb
(the coefficient of ii).

Real part a=a =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

3

Compute (1−6i)+(4+2i)(1 - 6i) + (4 + 2i) and write the result in the form
a+bia + bi.

Imaginary part bb (the coefficient of ii) ==   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

4

Compute (2+3i)(1−4i)(2 + 3i)(1 - 4i) and write the result in the form a+bia + bi.

Real part a=a =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

5

Compute (1+2i)2(1 + 2i)^2 and write the result in the form a+bia + bi.

Imaginary part bb (the coefficient of ii) ==   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

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