The Complex Plane flashcards
32 practice cards drawn from the The Complex Plane lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.
Read the The Complex Plane lessons in full →
Where does 1 + 4i sit?
1 across, 4 up
from “The Argand Diagram”
Where does 3 + 4i sit?
3 across, 4 up
from “The Argand Diagram”
|8 + 15i|
17
from “The Modulus of a Complex Number”
|5 + 12i|
13
from “The Modulus of a Complex Number”
What is the argument of 3?
0°
from “The Argument of a Complex Number”
What is the argument of 2 + 2i?
45°
from “The Argument of a Complex Number”
Multiply r=2 at 40° by r=5 at 20°
r=10 at 60°
from “Polar Form”
Multiply r=5 at 30° by r=2 at 30°
r=10 at 60°
from “Polar Form”
z = 3(cos 25° + i sin 25°). What are r and ?
r = 3,
from “The Form r(cos θ + i sin θ)”
Write r = 2 at 60° in full.
2(cos 60° + i sin 60°)
from “The Form r(cos θ + i sin θ)”
r=8 at 90° ÷ r=2 at 30°. What is the quotient’s modulus?
4
from “Dividing in Polar Form”
Divide r=12 at 60° by r=3 at 30°.
r=4 at 30°
from “Dividing in Polar Form”
Raise r=2 at 30° to the power 3.
r=8 at 90°
from “De Moivre’s Theorem”
Raise r=2 at 40° to the power 3.
r=8 at 120°
from “De Moivre’s Theorem”
How many cube roots does 1 have?
3
from “The Roots of Unity”
How far apart do the three cube roots of 1 sit?
120°
from “The Roots of Unity”
The roots of are the vertices of which shape?
a regular hexagon
from “Regular Polygons from the Roots of Unity”
How many degrees apart do the roots of sit?
45°
from “Regular Polygons from the Roots of Unity”
Matching the i parts of gives
from “Multiple Angles by De Moivre”
Why does one equation between complex numbers give two real results?
the real and i parts must match separately
from “Multiple Angles by De Moivre”
. What is ?
from “The Identity z + 1/z = 2 cos θ”
. What is ?
from “The Identity z + 1/z = 2 cos θ”
C + iS . Which part of that quotient is C?
the real part
from “Summing a Series with De Moivre”
Why is not geometric by itself?
consecutive cosines have no common ratio
from “Summing a Series with De Moivre”
Write in exponential form.
from “The Exponential Form of a Complex Number”
What is ?
−1
from “The Exponential Form of a Complex Number”
How far apart do the four fourth roots of a complex number sit?
90°
from “The nth Roots of a Complex Number”
What is the modulus of each cube root of 8i?
2
from “The nth Roots of a Complex Number”
Where is the center of |z − 2 + 3i| = 4?
2 − 3i
from “Circles and Bisectors on the Argand Diagram”
Which locus is a straight line?
|z − a| = |z − b|
from “Circles and Bisectors on the Argand Diagram”
What does arg(z − 2) = 60° draw?
a half-line out from 2
from “Rays and Regions on the Argand Diagram”
How is the boundary of |z| < 4 drawn?
dashed, because the rim is left out
from “Rays and Regions on the Argand Diagram”