Review worksheet
Pre-Calc
Solve the following by graphing
1. Simplify the following:
a. √(−64)
b. (−4 + 5𝑖) + (−1 − 2𝑖)
c. (-4 + 5i) – (-1 – 2i)
2+3𝑖
d.
3−4𝑖
2. Describe the geometric effect of the operation of :
a. (3 − 2𝑖) + (−2 + 4𝑖)
b. Given T(z) = z, what is the geometric effect when T(z) = i (z) :
3. Consider two complex numbers 𝐴 = −4+5𝑖 and 𝐵 = 4−10𝑖.
a. Find the midpoint of 𝐴 and 𝐵.
b. Find the distance between 𝐴 and 𝐵.
4. Convert z = 4 + 3i to trig form. (10 points):
1. Find r. r  a 2  b 2
b
2. Find  .   tan 1  
a
3. Fill in the blanks in z  r  cos   i sin  
5. Convert 4(cos 30 + i sin 30) to rectangular form. (10 points):
1. Evaluate the sin and cos
2. Distribute in r