if z=1-i,find the imaginary part of z6.
Answers
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3
Answer:
z=1+i
3
z
6
=(1+
3
)
6
using Binomial Theorem.
=
6
C
0
+
6
C
1
(i
3
)+
6
C
2
(i
3
)
2
+
6
C
3
(i
3
)
3
+
6
C
4
(i
3
)
4
+
6
C
5
(i
3
)
5
+
6
C
6
(i
3
)
6
=
6
C
0
+
6
C
2
(3)+
6
C
4
(9)−
6
C
6
(27)+i
3
(
6
C
1
−3
6
C
3
+9
6
C
5
)
=(1−15×3+135−27)+i
3
(60−60)
=(136−72)+i
3
(0)=64
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