Fsc Part 1 Mathematics (Complete Solution)

Q14
Find the multiplicative inverse of each of the following numbers

(i) (-4,7)

SOLUTION:(-4,7)

=
1
(-4,7)
=
1
(-4,7)
x
(-4,-7)
(-4,-7)
=
(-4,-7)
[(-4)(-4)-(7)(-7),(-4)(-7)+(-4)(7)]
=
(-4,-7)
(16+49,28-28)
=
(-4,-7)
(65,0)

therefore (65,0)=65

=
(-4,-7)
65
= -
4
65
, -
7
65

(ii) (√  2  ,-  5  )

SOLUTION:multiplicative inverse of complex number Z=(a,b) is  Z-1=

  (
a
a2+b2
,
-b
a2+b2
)

therefore the multiplicative inverse of (√  2 ,-  5 ) 

= (
 2
(√  2  )2+(-  5 )2
,
-(  5 )
(√  2  )2+(-  5 )2
)
= (
 2
2+ 5
,
 5
2+ 5
)
= (
 2
7
,
 5
7
)

(iii) (1,0)

SOLUTION:multiplicative inverse of complex number Z=(a,b) is  Z-1=

  (
a
a2+b2
,
-b
a2+b2
)

therefore multiplicative inverse of (1,0) is

=   (
1
(1)2+(0)2
,
-0
(1)2+(0)2
)
=   (
1
1
,
0
1
)

= (1,0)

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