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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 35
Total: 52
Reduce (
1
1−4i
−
2
1+i
) to the standard form.
Solution:  
We have , (
1
1−4i
−
2
1+i
) =
1+i−2(1−4i)
(1−4i)(1+i)
=
1+i−2+8i
1+i−4i+4
 =
−1+9i
5−3i
⇒ (
1
1−4i
−
2
1+i
)(
3−4i
5+i
) = (
−1+9i
5−3i
)(
3−4i
5+i
)
=
−3+4i+27i+36
25+5i−15i+3
 =
33+31i
28−10i
×
28+10i
28+10i
 =
924+330i+868i−310
784+100
=
614+1198i
884
 =
614
884
 +
1198
884
 i =
307
442
+
599
442
 i
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