# Exercise 5.2 (Complex number)

Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2.(Exercise 5.2 complex no. ncert math solution class 11)

Question 1:

Solution : Let

Comparing the real and imaginary parts, we have

Squaring and adding equation (1) and (2), we have

Therefore, modulus

Now, dividing equation (2) by (1), we have

From the equations (1), (2) and (3), it is clear that and are negative but is positive. So, lies in III quadrant. Therefore,

Argument

Question 2:

Solution : Let

Comparing the real and imaginary parts, we have

Squaring and adding equation (1) and (2), we have

Therefore, modulus

Now, dividing equation (2) by (1), we have

From the equations (1), (2) and (3), it is clear that and are negative but is positive. So, lies in II quadrant. Therefore,

Convert each of the complex numbers given in Exercises 3 to 8 in the polar form:

Question 3:

Solution : Let

Comparing the real and imaginary parts, we have

Squaring and adding equation (1) and (2), we have

Therefore, modulus

Now, dividing equation (2) by (1), we have

From the equations (1), (2) and (3), it is clear that and are negative but is positive. So, lies in IV quadrant. Therefore,

Therefore, the polar form of is

Question 4:

Solution : Let

Comparing the real and imaginary parts, we have

Squaring and adding equation (1) and (2), we have

Therefore, modulus

Now, dividing equation (2) by (1), we have

From the equations (1), (2) and (3), it is clear that and are negative but is positive. So, lies in II quadrant. Therefore,

Therefore, the polar form of is

Question 5:

Solution : Let

Comparing the real and imaginary parts, we have

Squaring and adding equation (1) and (2), we have

Therefore, modulus

Now, dividing equation (2) by (1), we have

From the equations (1), (2) and (3), it is clear that and are negative but tan is positive. So, lies in III quadrant. Therefore,

Therefore, the polar form of is given by

Question 6:

Solution : Let

Comparing the real and imaginary parts, we have

Squaring and adding equation (1) and (2), we have

Therefore, modulus

Now, dividing equation (2) by (1), we have

From the equations (1), (2) and (3), it is clear that and are 0 but is negative. Therefore,

Therefore, the polar form of is

Question 7:

Solution : Let

Comparing the real and imaginary parts, we have

Squaring and adding equation (1) and (2), we have

Therefore, modulus

Now, dividing equation (2) by (1), we have

From the equations (1), (2) and (3), it is clear that and all are positive. So, lies in I quadrant. Therefore,

Therefore, the polar form of is

Question 8:

Solution : Let

Comparing the real and imaginary parts, we have

Squaring and adding equation (1) and (2), we have

Therefore, modulus

Now, dividing equation (1) by (2), we have

From the equations (1), (2) and (3), it is clear that and are 0 but is positive. Therefore,

Therefore, the polar form of is given by

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