Fsc Part 1 Mathematics (Complete Solution)

Q2
Find the multiplicative inverse of each of the following numbers

(i) -3ι

SOLUTION:-Let  A=3ι

=(0,-3)

the multiplicative inverse of(0,-3)

= (
0
(0)2+(-3)2
,
-(-3)
(0)2+(-3)2
)
= (
0
0+9
,
3
0+9
)
= (
0
9
,
3
9
)
= ( 0 ,
1
3
)
=
ι
3

(ii) 1-2ι

SOLUTION:Let B=1-2ι

=(1,-2)

the multiplicative inverse of (1,-2)

= (
1
(1)2+(-2)2
,
-(-2)
(1)2+(-2)2
)
= (
1
1+4
,
2
1+4
)
= (
1
5
,
2
5
)
=
1
5
+
5
 

(iii) -3-5ι

SOLUTION:Let C=-3-5ι

=(-3,-5)

therefore multiplicative inverse of (-3,-5)

= (
-3
(-3)2+(-5)2
,
-(-5)
(-3)2+(-5)2
)
= (
-3
9+25
,
5
9+25
)
= (
-3
34
,
5
34
)
= -
3
34
+
34
)

(iv) (1,2)

SOLUTION:

multiplciative inverse of (1,2)

= (
1
(1)2+(2)2
,
-(2)
(1)2+(2)2
)
= (
1
1+4
,
-2
1+4
)
= (
1
5
,
-2
5
)
=
1
5
_
5
 

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