3
(iii) Observe that
(3 3)2 + 32 = 36 = 6; so (3 3 + 3i) = 6(cos + i sin ). Hence
6
6
(3 3 + 3i)3 = 6(cos + i sin )
6
6
8.
3
= 63 (cos + i sin ) = 63 (0 + i) = 216i.
2
2
We use the shorthand notation cis = cos + i sin throughout this question, writing
z =
MATH1001 Dierential Calculus
Practice Questions for Quiz 1
The rst quiz will be held during tutorials in week starting on May 6. The material
tested will come from Chapters 2, 3, 4, 5 and 6.
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Practice Questions for Quiz 2, MATH1001
Quiz 2 is intended to assess lecture material from weeks 8 to 10, (corresponding to tutorials in weeks 9
to 11). This material can be found in written form in the course notes, chapters 8 to 10. The second
quiz will
Practice Questions for Quiz 2, MATH1001
Quiz 2 is intended to assess lecture material from weeks 8 to 10, (corresponding to tutorials in weeks 9
to 11). This material can be found in written form in the course notes, chapters 8 to 10.
Note that in the qui
THE UNIVERSITY OF SYDNEY
M ATH 1001 D IFFERENTIAL C ALCULUS
Assignment 1
Semester 1
1. Consider the complex number z =
2012
i201 + i8
.
i3 (1 + i)2
(a) Show that z can be expressed in the Cartesian form
1 1
+ i.
2 2
(2 marks)
(b) Find the modulus of 4z 2.