Consider the complex number 2 + i. Working in exponential form, investigate the effect of multiplying successively, four times, by i. Plot the numbers on an Argand diagram. 11.
Consider the complex number 2 + i. Working in exponential form, investigate the effect of multiplying successively, four times, by i. Plot the numbers on an Argand diagram. 11.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 11
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Worksheet 6 - Comple...
(a) z– 3w (b) (c) zw
(d)
(e) Ju|
2.
Solve the equations:
(a) 3v2 + 2v +1=0
(b) 3x? - 4x + 8 = 0
3.
One root of the equation x-8x2 + 4x - 32 = 0 is 21. Find the remaining
roots.
State the real and imaginary parts of the complex number z =;
4.
5.
Find the complex numbers z which satisfy the equations:
(a) 2(z – 2) + zž = 2(13 – 101) (b) 2z – i+ 7 – 2i = 0
6.
Verify the following for general complex numbers z = a + ib and w = c + id.
(a) Re(2) = (b) Im(2) = (c) zw = żw (d) H-
7.
For z = cos 0 + i sin 0, show that = cos 20 +i sin 20.
8.
Express the following complex numbers in polar form and plot them on an
Argand diagram.
(a) 12 + 5i
(b) v3-i
(c) -1-1
9.
Express the following numbers in exponential form and plot them on an
Argand diagram.
(a) 1+ v3i
(b) -1+i
(c) -1
10.
Convert 1– 3i and 5 + i into exponential form and hence calculate the
modulus and argument of:
(a) 1-30
(b) (1- 31)-
1
5+1
Consider the complex number 2 + i, Working in exponential form, investigate
the effect of multiplying successively, four times, by i. Plot the numbers on
Argand diagram.
11.
12.
Express the following in Cartesian form.
(a) Seim
(b) -2elm/3
(c) e-l2n/3eim/6
13.
Solve the following equations, giving your answers in Cartesian form.
(a) z* +1 = 0
(b) z -i = 0
Answers
1.
(a) 9-161 (b) 금(3+0 (c)-11-131 (d) 습(-11+ 130) (e)
29
(a) v =(-1+ vZi)
(b) x =(2+ 2V51)
2.
3.
the three roots are x = 8,2i, -2i
Re(2) =. Im(2) =
4.
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