CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths
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Exercise 5.2
Question 1:
Find the modulus and the argument of the complex number z 1
i 3
Solution 1:
z 1
i 3
r cos 1
r sin 3
Let
and
On squaring and adding, we obtain
2 2 2
rcos rsin 1
3 2
2 2 2
r
cos sin 1 3
2 2 2
r
r
4 2
4
cos sin 1
Modulus = 2
2cos
1
1
cos
2
Conventionally, r 0
and 2sin 3
and
3
sin
2
Since both the values of
quadrant,
Argument
sin
2
3
3
and
cos
negative and
Thus, the modulus and argument of the complex number
sin
1
3i
and
cos
are 2 and
are negative in III
2
3
respectively.
Question 2:
Find the modulus and the argument of the complex number z 3 i
Solution 2:
z 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
3 1 4
cos sin 1
2 2 2
r