Let z be the complex number 2 + 3i lying in the complex plane.
a. what is the conjugate of z? explain how it is related geometricaly to z.
b. write down the complex number that is the reflection of z acros the vertical axis. explain how you
determined your answer.
let mm be the line through the origin of slope 1
2 in the complex plane.
c. write down a complex number, of modulus 1 that lies on mm in the first quadrant in rectangular
form.
d. what is the modulus of
e. explain the relationship betwen and z. first, use the properties of modulus to answer this
question, and then give an explanation involving transformations.
f. when asked,
"what is the argument of 1

z? "
paul gave the answer arctan
− arctan
which he then computed to two decimal places.
provide a geometric explanation that yields paul’s answer.