# Maths sheet 1 .pdf

### File information

Title: Complex Numbers sheet
Author: mufic

This PDF 1.5 document has been generated by Microsoftรยฎ Word 2013, and has been sent on pdf-archive.com on 06/11/2015 at 09:11, from IP address 41.37.x.x. The current document download page has been viewed 417 times.
File size: 323.86 KB (2 pages).
Privacy: public file

### Document preview

Complex Numbers sheet
1) Find the output of the following operations performed on complex numbers
2+๐
๐)
๐+1
d (

2

โ3โ ๐

g)

10

+

1
๐

10

)

(2 + ๐)(1 โ ๐)
3โ2๐

j) (โ2 โ 3 ๐) (โ3 + 4๐)

(1โ๐ )6

b) (1 โ โ3 ๐)

c)

e) (1 + ๐)5

f) (1 + โ3 ๐) (๐ โ 1)7

h)

1
๐(3+2๐)2
(โ2โ3 ๐)

k)

(โ3+4๐)

(๐+1)7
5

i)

l)

(โ3+โ2 ๐)3
(โ2โโ3๐)
1
(โ3+4๐)

2) Find the modulus ( |Z |) and the argument ( arg(Z) ) for next complex numbers

3)

๐) ๐ = (1 โ ๐)

b) ๐ = 11๐

c) ๐ = โ

d) ๐ = (โ2 + 2โ3๐)

e) ๐ = โ4๐

f) ๐ =

๐
4

1
2

Find the roots of complex numbers where

๐) ๐ 3 = โ8

d)

๐ 4 = (โ2 โ 2โ3๐)

b) ๐ 3 = 27๐

e)

๐ 3 = 4โ2๐ โ 4โ2

1

c) ๐ 2 = (โ1 + โ3 ๐)

f) ๐ 6 = 64๐

Complex Numbers sheet
g) ๐ 6 = โ64๐
j) ๐ 3 =

โ2
2

โ

4

h) ๐ 8 = โ16

โ2
2

1
2

i) ๐ = โ

โ3

๐

4) Given Z= cos(3) + sin(3) ๐ prove that 1 + ๐ง = (1 + ๐ง)๐ง
5) Calculate (cos(2) + sin(2)๐ + 1)๐
6) Given : n is a positive integer
Z is a complex number with modulus 1, such that ๐ง 2๐ โ  โ1
show that

๐ง๐

1+๐ง 2๐

is a real number.

7) Let ๐ง the conjugate complex number of z. find z such that

๐ง 2 + (๐ง)2 = ๐ง๐๐๐
8) Find the value of k for the quotient

(2โ๐๐)
(๐โ๐)

if it is :

- A pure imaginary number
- A real number
9) The complex number, 2 + 2
is rotated 45ยฐ about the origin of its
coordinates in an anti-clockwise direction. Find the complex number
obtained after the turn.

10)

Determine the value of b for the quotient

, if it equals:

Note the following trigonometric Identities
a) cos 2 ๐ฅ + sin2 ๐ฅ = 1
b) cos(2๐ฅ) = cos 2 ๐ฅ โ sin2 ๐ฅ = 2 cos 2 ๐ฅ โ 1 = 1 โ 2 sin2 ๐ฅ
c) sin(2๐ฅ) = 2sin(๐ฅ)cos(๐ฅ)

2

2

๐

Maths sheet-1.pdf (PDF, 323.86 KB)

### Share on social networks

#### HTML Code

Copy the following HTML code to share your document on a Website or Blog