Operations with Complex Numbers

What does i² = ?

• -1
• √-1
• 1
• -√1

Tags

CCSS.HSN.CN.A.1

Reorder the following

• 24 -24i -12i + 12i²

• 24 -24i -12i + 12(-1)

• 24 -24i -12i - 12

  = 12 - 36i

• 8(3 - 3i) - 4i(3 - 3i)

Reorder the following

• 8(-4 -7i) - 3i(-4 -7i)

• -32 - 56i + 12i -21

  = -53 - 44i

• -32 - 56i + 12i + 21i²

• -32 - 56i + 12i + 21(-1)

What is the simplified form of (-3 + 2i)(1- 4i)

• Multiply

  -3 + 12i + 2i - 8i²

• Combine Like Terms

  5 + 14i

• Rewrite to distribute

  -3(1 - 4i) +2i(1 - 4i)

• Multiply -8 by -1

  -3 + 12i + 2i + 8

• Replace i² with -1

  -3 + 12i + 2i - 8(-1)

What is the simplified form of (-6i)(3i)

• -18(-1) = -18

• -6⋅3⋅i⋅i = -18i

• -18i² = -18(-1) = 18

• -6⋅3⋅i⋅i = -18i²

(3+4i)(-8-i)

• -24 -3i - 32i - 4i²

• -24 -3i - 32i + 4

• 3(-8 - i) + 4i(-8 - i)

• -20-35i

• -24 -3i - 32i - 4(-1)

• Rewrite to distribute

  4(4 + i) - 5i(4 + i)

• Replace i² with -1

  16 + 4i - 20i - 5(-1)

• Multiply

  16 + 4i - 20i - 5i²

• Combine Like Terms

  21 - 16i

• Multiply -5 by -1

  16 + 4i - 20i + 5

Find the Product, product means you are multiplying the complex numbers in the parenthesis

• -3(-6 -8i) + 2i(-6 -8i)

• 18 + 24i -12i - 16i²

• 18 + 24i -12i + 16

  = 34 + 12i

• 18 + 24i -12i - 16(-1)

Find the complex product

• 8 + 4i + 10i - 5

• 3 + 14i

• 8 + 4i + 10i + 5i²

• Write in complex standard form which is with the real part first

  9 + 6i

• Multiply each by 3i

  6i - 9i²

• i² = -1 so replace it

  6i - 9(-1)

• Multiply -9 by -1

  6i + 9