Complex Numbers – Addi2on, Subtrac2on and Mul2plica2on
1. Let 𝑤 = 5 + 2𝑖 and 𝑧 = 3 + 𝑖. Find
a. 𝑤 + 𝑧
b. 𝑤 − 𝑧
c. 𝑤𝑧
2. Let 𝑤 = 7 − 2𝑖 and 𝑧 = −1 + 3𝑖. Find
a. 𝑤 + 𝑧
b. 𝑤 − 𝑧
c. 𝑤𝑧
3. Let 𝑤 = −3 + 2𝑖 and 𝑧 = −1 − 𝑖. Find
a. 2𝑤 + 3𝑧
b. 4(𝑤 − 𝑧)
c. 𝑤𝑧
4. Let 𝑤 = 1 + 𝑖. Find
a. 𝑤 !
b. 𝑤 "
c. 𝑤 #
5. Let 𝑤 = 3 + 4𝑖 and 𝑤 ∗ = 3 − 4𝑖. Find
a. 𝑤 + 𝑤 ∗
b. 𝑤𝑤 ∗
6. Let 𝑤 = −2 + 𝑖 and 𝑤 ∗ = −2 − 𝑖. Find
a. 𝑤 + 𝑤 ∗
b. 𝑤𝑤 ∗
7. Given 𝑓(𝑧) = 𝑧 ! − 2𝑧 + 5. Show that
a. 𝑓(1 + 2𝑖) = 0
b. 𝑓(1 − 2𝑖) = 0
8. Given 𝑔(𝑧) = 𝑧 ! − 4𝑧 + 13.
a. Show that 𝑔(2 + 3𝑖) = 0
b. Suggest a complex number that could be the other soluCon to 𝑔(𝑧) = 0
9. Given ℎ(𝑧) = 𝑧 ! + 10𝑧 + 26.
a. Show that ℎ(−5 + 𝑖) = 0
b. Suggest a complex number that could be the other soluCon to ℎ(𝑧) = 0