CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths
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3 2
1 i 3i 3i
1 i 3i
3
2
2i
22i
Question 2:
For any two complex numbers
Re
z 1
z z Re z Re z Im z Im z
1 2 1 2 1 2
Solution 2:
Let
z x iy
1 1 1
and
z x iy
2 2 2
z z x iy x iy
1 2 1 1 2 2
x x iy iy x iy
1 2 2 1 2 2
x x ix y iy x i y y
2
1 2 1 2 1 2 1 2
and
z 2
, prove that
2
x1x 2
ix1 y2 iy1x2 y1 y
2 i
1
x x y y i x y y x
1 2 1 2 1 2 1 2
Re z z x x y y
1 2 1 2 1 2
Re z z Re z Re z Im z Im z
Hence, proved.
1 2 1 2 1 2
Question 3:
Reduce
Solution 3:
1 2 3 4i
1 4i 1 i 5 i
1 i 21
4i
1 2 34i
34i
1 4i 1 i 5 i 1 4i 1 i
5 i
1 i 2 8i 3 4i 1 9i 3 4i
2
1 i 4i 4i
5 i
5 3i
5 i
2
3 4i 27i 36i 33 31i 33 31i
2
25 5i 15i 3i
28 10i 2 14 5i