CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths
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r 4 2
Modulus = 2
2cos
3
and 2sin 1
3 1
cos
and sin
2 2
5
6 6
Conventionally, r 0
Thus, the modulus an argument of the complex number
[As lies in the II quadrant]
3 i
are 2 and
5
6
respectively.
Question 3:
Convert the given complex number in polar form: 1 i
Solution 3:
1i
r cos 1
r sin 1
Let and
On squaring and adding, we obtain
r
2 2 2 2 2
2
cos r sin 1 1
2 2 2
r
r
2
cos sin 1 1
2
r 2 Conventionally, r
0
2 cos
1
cos
4
1
2
and
and
2 sin 1
sin
1
2
As liesin the IV quadrant
1i r cos
i r sin
2 cos i 2 sin 2 cos isin
4 4
4 4
This is the required polar form.