Operations with Imaginary Numbers

​Learning Goals

• ​Let’s work with complex numbers.

• Let's multiply complex numbers.​

​Learning Targets

• I can add complex numbers and calculate powers of imaginary numbers.

• I can multiply complex numbers.​

​complex number

​A number in the complex plane. It can be written as a + bi, where a and b are real numbers and i² = -1.

​imaginary number

​A number on the imaginary number line. It can be written as bi, where b is a real number and i² = -1.

Open Ended

Find the value of these expressions mentally.

2 - 2 + 20 - 20 + 200 - 200

Open Ended

Find the value of these expressions mentally.

100 - 50 + 10 - 10 + 50 - 100

Open Ended

Find the value of these expressions mentally.

3 + 2 + 1 + 0 - 1 - 2 - 3

Open Ended

Find the value of these expressions mentally.

1 + 2 + 4 + 8 + 16 + 32 - 16 - 8 - 4 - 2 - 1

Open Ended

This diagram represents (2 + 3i) + (-8 - 8i).

How do you see 2 + 3i represented?

Open Ended

This diagram represents (2 + 3i) + (-8 - 8i).

How do you see -8 - 8i represented?

Open Ended

This diagram represents (2 + 3i) + (-8 - 8i).

What complex number does A represent?

Open Ended

Write these sums and differences in the form a + bi, where a and b are real numbers.

(-3 + 2i) + (4 - 5i)

Open Ended

Write these sums and differences in the form a + bi, where a and b are real numbers.

(-37 - 45i) + (11 + 81i)

Open Ended

Write these sums and differences in the form a + bi, where a and b are real numbers.

(-3 + 2i) - (4 - 5i)

Open Ended

Write these sums and differences in the form a + bi, where a and b are real numbers.

(-37 - 45i) - (11 + 81i)

Open Ended

Evaluate 2i, (2i)², (2i)³, and (2i)⁴ write in the form a + bi if necessary.

Open Ended

K = 3 - 4i and m = -2 + 9i. Write each expression in the form a + bi, where a and b are real numbers:

k + m

Open Ended

K = 3 - 4i and m = -2 + 9i. Write each expression in the form a + bi, where a and b are real numbers:

k - m

Open Ended

Write -(3i)³ in the form a + bi, where a and b are real numbers.

Fill in the Blanks

Evaluate 4i ⦁ 3i

Fill in the Blanks

Evaluate 4i ⦁ -3i

Fill in the Blanks

Evaluate -2i ⦁ -5i

Fill in the Blanks

Evaluate -5i ⦁ 5i

Fill in the Blanks

Evaluate (-5i)²

Draw

Match an expression in column A with an equivalent expression in column B.

Open Ended

Simplify the expression:

(3 + 9i)(5i)

Open Ended

Simplify the expression:

(8 + i)(-5 + 3i)

Open Ended

Simplify the expression:

(3 + 2i)²

Open Ended

Simplify the expression:

(3 + 2i)²

​Learning Targets

• I can add complex numbers and calculate powers of imaginary numbers.

• I can multiply complex numbers.​