De Moivre’s Theorem cos sin cos sin for all integers n i n i n n
X2 t01 09 de moivres theorem
Jun 15, 2015
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De Moivre’s Theorem cos sin cos sin
for all integers
ni n i nn
De Moivre’s Theorem cos sin cos sin
for all integers
ni n i nn
ninrir nn sincossincos
this extends to;
De Moivre’s Theorem cos sin cos sin
for all integers
ni n i nn
ninrir nn sincossincos
this extends to;
5. . 1e g i
De Moivre’s Theorem cos sin cos sin
for all integers
ni n i nn
ninrir nn sincossincos
this extends to;
5. . 1e g i 2
11 22
z
4
11tanarg 1
z
De Moivre’s Theorem cos sin cos sin
for all integers
ni n i nn
ninrir nn sincossincos
5
42
cis
this extends to;
5. . 1e g i 2
11 22
z
4
11tanarg 1
z
De Moivre’s Theorem cos sin cos sin
for all integers
ni n i nn
ninrir nn sincossincos
5
42
cis
this extends to;
5. . 1e g i 2
11 22
z
452 5 cis
4
11tanarg 1
z
De Moivre’s Theorem cos sin cos sin
for all integers
ni n i nn
ninrir nn sincossincos
5
42
cis
this extends to;
5. . 1e g i 2
11 22
z
452 5 cis
4
11tanarg 1
z
4324 cis
De Moivre’s Theorem cos sin cos sin
for all integers
ni n i nn
ninrir nn sincossincos
5
42
cis
this extends to;
5. . 1e g i 2
11 22
z
452 5 cis
4
11tanarg 1
z
4324 cis
43sin
43cos24 i
51 i
De Moivre’s Theorem cos sin cos sin
for all integers
ni n i nn
ninrir nn sincossincos
5
42
cis
this extends to;
5. . 1e g i 2
11 22
z
452 5 cis
4
11tanarg 1
z
4324 cis
43sin
43cos24 i
i
21
2124
i44
51 i
Finding Rootsrcisziyxz
n
n
If
1,,1,0 2
nknkcisrz n
Finding Rootsrcisziyxz
n
n
If
1,,1,0 2
nknkcisrz n
izige 4 .. 2
Finding Rootsrcisziyxz
n
n
If
1,,1,0 2
nknkcisrz n
izige 4 .. 2
242 cisz
Finding Rootsrcisziyxz
n
n
If
1,,1,0 2
nknkcisrz n
izige 4 .. 2
242 cisz
1,0 2
22
2
k
kcisz
Finding Rootsrcisziyxz
n
n
If
1,,1,0 2
nknkcisrz n
izige 4 .. 2
242 cisz
1,0 2
22
2
k
kcisz
452,
42 ciscisz
Finding Rootsrcisziyxz
n
n
If
1,,1,0 2
nknkcisrz n
izige 4 .. 2
242 cisz
1,0 2
22
2
k
kcisz
452,
42 ciscisz
iiz
21
212,
21
212 iiz 22,22
Finding Rootsrcisziyxz
n
n
If
1,,1,0 2
nknkcisrz n
izige 4 .. 2
242 cisz
1,0 2
22
2
k
kcisz
452,
42 ciscisz
iiz
21
212,
21
212 iiz 22,22
y
x
OR
Finding Rootsrcisziyxz
n
n
If
1,,1,0 2
nknkcisrz n
izige 4 .. 2
242 cisz
1,0 2
22
2
k
kcisz
452,
42 ciscisz
iiz
21
212,
21
212 iiz 22,22
y
x
OR2
4cis
Finding Rootsrcisziyxz
n
n
If
1,,1,0 2
nknkcisrz n
izige 4 .. 2
242 cisz
1,0 2
22
2
k
kcisz
452,
42 ciscisz
iiz
21
212,
21
212 iiz 22,22
y
x
OR2
4cis
324
cis
4 16 0ii x
4 16 0ii x 4 16x 4 16 0x cis
4 16 0ii x 4 16x 4 16 0x cis
22 0,1,2,34kx cis k
4 16 0ii x 4 16x 4 16 0x cis
22 0,1,2,34kx cis k
32 0,2 ,2 ,22 2
x cis cis cis cis
4 16 0ii x 4 16x 4 16 0x cis
22 0,1,2,34kx cis k
32 0,2 ,2 ,22 2
x cis cis cis cis
2,2 , 2, 2x i i
4 16 0ii x 4 16x 4 16 0x cis
22 0,1,2,34kx cis k
32 0,2 ,2 ,22 2
x cis cis cis cis
2,2 , 2, 2x i i
y
x
OR
4 16 0ii x 4 16x 4 16 0x cis
22 0,1,2,34kx cis k
32 0,2 ,2 ,22 2
x cis cis cis cis
2,2 , 2, 2x i i
y
x
OR
2 0cis
4 16 0ii x 4 16x 4 16 0x cis
22 0,1,2,34kx cis k
32 0,2 ,2 ,22 2
x cis cis cis cis
2,2 , 2, 2x i i
y
x
OR
2 0cis
22
cis
2cis
22
cis
4 16 0ii x 4 16x 4 16 0x cis
22 0,1,2,34kx cis k
32 0,2 ,2 ,22 2
x cis cis cis cis
2,2 , 2, 2x i i
y
x
OR
2 0cis
22
cis
2cis
22
cis
Cambridge: Exercise 7A; 1, 2, 3 abef, 5, 6, 7,
9 to 14, 16 to 18
Patel: Exercise 4E; 1 to 4 ac
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