Grade 11 · Math · Algebra 2

11th grade Complex conjugates, and dividing complex numbers worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Complex conjugates, and dividing complex numbers

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Jun works out (4 − i) ÷ (2 + 3i). Write the answer in a + bi form, with fractions. What is (4 − i) ÷ (2 + 3i)?
Kira's robot divides 1 + 4i by 3 − i. What is (1 + 4i) ÷ (3 − i) in a + bi form?
Luz divides two grid map pins. Write the answer in a + bi form, with fractions. What is (-2 + i) ÷ (3 + 4i)?
Milo has a puzzle: (1 + i) times a number is 4 + 2i. What is the number, in a + bi form?
Noah's robot multiplied a number by 2 − i and got 5. What was the number, in a + bi form?
Pia writes a riddle: (3 + i) times a number is 10i. What is the number, in a + bi form?
Tala finds the number that multiplies 3 + 4i to make 1. What is 1 ÷ (3 + 4i) in a + bi form?
Zee writes 1 ÷ (1 − 2i) on the board. Write it in a + bi form, with fractions. What is 1 ÷ (1 − 2i)?
Esme's robot needs the reciprocal of 2 + i. What is 1 ÷ (2 + i) in a + bi form?
Jun finds the reciprocal of a grid map pin, -1 + 3i. What is 1 ÷ (-1 + 3i) in a + bi form?

Complex conjugates, and dividing complex numbers. Every version has 10 questions, and the answer key prints on the second page.

I can write a conjugate by flipping a point across the real axis.
I can multiply a number by its conjugate and get a real number.
I can divide complex numbers by multiplying the top and bottom by the conjugate of the bottom.

Standard: N-CN.A.3 (+)

conjugate: The mirror image across the real axis: a + bi becomes a − bi.

real axis: The across line through 0.

reciprocal: The number that multiplies to make 1.

denominator: The bottom of a fraction.

Your child changed the sign of the real part to make the conjugate.

Your child changed both signs, which is the opposite number, not the conjugate.

Your child used i² = 1 instead of i² = -1.

Ask: when a point is flipped across the across line, which part changes?

Ask: does a flip across the across line move a point left or right?

Ask: what is i × i?

What is the most common mistake with complex conjugates, and dividing complex numbers?

Your child changed the sign of the real part to make the conjugate.

How can I help my child with complex conjugates, and dividing complex numbers?

Ask: when a point is flipped across the across line, which part changes?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records