Fsc Part 1 Mathematics (Complete Solution)

Q3
SIMPLIFY

(i) ι101

SOLUTION:

ι101100

= (ι2)50

= (-1)50[ ∴  ι2=-1]

= (1) .ι   

= ι

(ii) (-aι)4,    a∈R

SOLUTION:

(-aι)4=(-a)4.(ι)4

= a4.(ι2)2

= a4.(-1)2[ ∴  ι2=-1]

= a4.(1)

= a4

(iii)ι-3

SOLUTION:

ι-3=(ι3)-1

= (ι2.ι)-1

= (-1.ι)-1[ ∴  ι2=-1]

= (-ι)-1

=-
1
ι
= -
1
ι
x
ι
ι
= -
ι
ι2
= -
ι
-1

= ι

(iv) ι-10

SOLUTION:

ι-10=[(ι)10]-1

= [(ι2)5]-1

= [(-1)5]-1[ ∴  ι2=-1]

= (-1)-1

= -1

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