CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths
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3
4
4
[As lies in the III quadrant]
3 3 3 3
1 i r cos
i r sin
2 cos i 2 sin 2 cos isin
4 4 4 4
This is the required polar form.
Question 6:
Convert the given complex number in polar form:
Solution 6:
3
r cos 3
r sin 0
Let
and
On squaring and adding, we obtain
r
2 2 2 2
2
cos r sin 3
2 2 2
r
r
2
cos sin 9
9
r 9 3
[Conventionally, r > 0]
and 3sin 0
3cos
3
cos
1
and sin 0
3 r cos i r sin 3cos i3sin 3 cos isin
This is the required polar form.
3
Question 7:
Convert the given complex number in polar form: 3 i
Solution 7:
3 i
Let
and rsin 1
On squaring and adding, we obtain
r
r cos 3
2
cos r sin 3 1
2 2 2 2 2
2 2 2
r
cos sin 3 1