Fsc Part 1 Mathematics (Complete Solution)

Q16
Separate into real and imaginary parts (write as a simple complex number.)

(i)
2-7ι
4+5ι

SOLUTION:

2-7ι
4+5ι

By Rationalizing

=
2-7ι
4+5ι
x
4-5ι
4-5ι
=
(2-7ι)(4-5ι)
(4+5ι)(4-5ι)
=
(2)(4)+(2)(-5ι)+(-7ι)(4)+(-7ι)(-5ι)
(4)2-(5ι)2
=
8-10ι-28ι+35ι2
(4)2-(5ι)2
=
8-38ι+35ι2
16-25ι2

by putting the value of ι2 , we get

=
8-38ι+35(-1)
16-25(-1)
=
8-38ι-35
16+25
=
-27-38ι
41
=-
27
41
-
38ι
41

(ii)
(-2+3ι)2
1+ι
SOLUTION:
(-2+3ι)2
1+ι
=
(-2)2+(3ι)2+2(-2)(3ι)
1+ι
=
4+9ι2-12ι
1+ι

put the value of ι2

=
4+9(-1)-12ι
1+ι
=
-5-12ι
1+ι

by rationalizing

=
-5-12ι
1+ι
x
1-ι
1-ι
=
(-5-12ι)(1-ι)
(1+ι)(1-ι)
=
(-5)(1)+(-5)(-ι)+(-12ι)(1)+(-12ι)(-ι)
(1+ι)(1-ι)
=
-5+5ι-12ι+12ι2
1-ι2
=
-5+5ι-12ι+12(-1)
1-(-1)
=
-17-7ι
2
= -
17
2
-
2
(iii)
ι
1+ι
SOLUTION:
ι
1+ι

BY Rationalizing

=
ι
1+ι
x
1-ι
1-ι
=
ι(1-ι)
(1+ι)(1-ι)
=
ι-ι2
1-ι2

Put the value of ι2

=
ι-(-1)
1-(-1)
=
ι+1
2
=
ι
2
+
1
2

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