7.2 Homework Problems: Introduction to Complex Numbers and Addition
1. Simplify the following using complex numbers
a. [latex]{i}^{33}[/latex]
b. [latex]{i}^2[/latex]
c. [latex]{i}^{100}[/latex]
d. [latex]{i}^{39}[/latex]
2. Express the following as complex numbers
a. [latex]\sqrt{-25}[/latex]
b. [latex]-\sqrt{-16}[/latex]
c. [latex]8\ +\ \sqrt{-16}[/latex]
d. [latex]-\sqrt{-4x^2}[/latex]
e. [latex]-25[/latex]
f. [latex]12\ \ +\ \sqrt{-81x^6}[/latex]
3. Plot the following rectangular coordinates on the graph
a. (-4 + 7i)
b. (-5 – 8i)
c. (-7 + j5)
d. (-4 + 7i)
e. (8 + j3)
4. Perform the requested operation and simplify as much as possible
a. (2.0 + 5.0i) + (5.0 – 3.0i)
b. (-4 + 7i) + (8 + 6i)
c. (9 – 9i) – (0 + 10i)
d. (0.52 + j1.85) – ( 2.14 – j0.91)
e. (5.0) + (1.5 – j2.4)