Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter5: Similar Triangles
Section5.2: Similar Polygons
Problem 11E: a Does the similarity relationship have a reflexive property for triangles and polygons in general?...
Related questions
Question
![1. Mark on an Argand diagram the points
representing the following numbers:
(a) 2 (b) 3i (c)-i (d) 1+2i (e) 3-i
(1) -2+3i
2. The points A, B, C and D represent the numbers
2₁, 22, 23 and 2, and O is the origin.
(a) If OABC is a parallelogram, and z₁=1+i,
2₂=4+5i, find 2₁.
(b) Find 2₂ and 2, when ABCD is a square and
(1) 2₁=2+1, 2,=6+7i
(ii) z₁=6-2i, 2=6i
3. Find the modulus and argument of
(a) 1-i (b) 1+√√3i (c) 3-3i (d) 3+2i
4. Show that
(a) ||-|| (b) argž=-argz
and illustrate these results on an Argand
diagram.
5. Find the modulus and argument of 2₁, 22, 2122
and when 2₁=1+i and 2₁= √3+i. What do
you notice?
6. Write in the form a+bi
(c) [3√/2,-34
(d) [4,13]
7. Write in polar form
(a) 1+i (b) -2+i (c)-5 (d) 4i (e) 3+4i
(f) -3-4i (g) 3-4i (h) -3+4i
8. In this question, angles are in radians.
(a) (i) Plot the following complex numbers on
an Argand diagram and label them:
2₁=[4.01.22-[3] [24]
Calculate zxz₁.2×2₂. etc. and plot the
points on the same diagram as in (i).
What do you notice?
(b) Repeat (a) (ii) using z = [14]
(c) In general, what happens when a complex
number is multiplied by [1.0]? Make up some
examples to illustrate your answer.
(d) Repeat (a) (ii) using z = [0.5.]
(e) In general, what happens when a complex
number is multiplied by [0.5.]? Make up
some examples to illustrate your answer.
(f) Repeat (e) for [3.]
(g) Describe what happens when a complex
number is multiplied by [3.] Make up
some examples to illustrate your answer.
(ii) Let the complex number z](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f03dc9e-b6dd-4d72-82ce-7ab24f78aa2a%2Fdb81bac8-23bd-4370-943e-d31ee2a2c088%2Fon0xng_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Mark on an Argand diagram the points
representing the following numbers:
(a) 2 (b) 3i (c)-i (d) 1+2i (e) 3-i
(1) -2+3i
2. The points A, B, C and D represent the numbers
2₁, 22, 23 and 2, and O is the origin.
(a) If OABC is a parallelogram, and z₁=1+i,
2₂=4+5i, find 2₁.
(b) Find 2₂ and 2, when ABCD is a square and
(1) 2₁=2+1, 2,=6+7i
(ii) z₁=6-2i, 2=6i
3. Find the modulus and argument of
(a) 1-i (b) 1+√√3i (c) 3-3i (d) 3+2i
4. Show that
(a) ||-|| (b) argž=-argz
and illustrate these results on an Argand
diagram.
5. Find the modulus and argument of 2₁, 22, 2122
and when 2₁=1+i and 2₁= √3+i. What do
you notice?
6. Write in the form a+bi
(c) [3√/2,-34
(d) [4,13]
7. Write in polar form
(a) 1+i (b) -2+i (c)-5 (d) 4i (e) 3+4i
(f) -3-4i (g) 3-4i (h) -3+4i
8. In this question, angles are in radians.
(a) (i) Plot the following complex numbers on
an Argand diagram and label them:
2₁=[4.01.22-[3] [24]
Calculate zxz₁.2×2₂. etc. and plot the
points on the same diagram as in (i).
What do you notice?
(b) Repeat (a) (ii) using z = [14]
(c) In general, what happens when a complex
number is multiplied by [1.0]? Make up some
examples to illustrate your answer.
(d) Repeat (a) (ii) using z = [0.5.]
(e) In general, what happens when a complex
number is multiplied by [0.5.]? Make up
some examples to illustrate your answer.
(f) Repeat (e) for [3.]
(g) Describe what happens when a complex
number is multiplied by [3.] Make up
some examples to illustrate your answer.
(ii) Let the complex number z
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