**Question 1.Find the modulus and amplitude for each of the following complex numbers:(i) 7 – 5iSolution:**

Let z = 7 – 5i

a = 7, b = -5

i.e. a > 0, b < 0

Here, (7, -5) lies in 4th quadrant.

**(ii) √3 + √2 iSolution:**

Let z = √3 + √2 i

a = √3, b = √2,

i.e. a > 0, b > 0

**(iii) -8 + 15iSolution:**

Let z = -8 + 15i

a = -8, b = 15 , i.e. a < 0, b > 0

**(iv) -3(1 – i)Solution:**Let z = -3(1 – i) = -3 + 3i

a = -3, b = 3 , i.e. a < 0, b > 0

**(v) -4 – 4iSolution:**

Let z = -4 – 4i

a = -4, b = -4 , i.e. a < 0, b < 0

**(vi) √3 – iSolution:**Let z = √3 – i

a = √3, b = -1, i.e. a > 0, b < 0

**(vii) 3Solution:**Let z = 3 + 0i

a = 3, b = 0

z is a real number, it lies on the positive real axis.

and amp (z) = 0

**(viii) 1 + iSolution:**

Let z = 1 + i

a = 1, b = 1, i.e. a > 0, b > 0

**(ix) 1 + i√3Solution:**

Let z = 1 + i√3

a = 1, b = √3, i.e. a > 0, b > 0

Solution:

**Question 3.**

The above complex numbers will be represented by the points

A (3, 5), B (3, -5), C (-3, -5) , D (-3, 5) respectively as shown below:

**Question 4.Express the following complex numbers in polar form and exponential form.(i) -1 + √3 iSolution:**

Let z = – 1 + √3

a = -1, b = √3

**(ii) -iSolution:**

Let z = -i = 0 – i

a = 0, b = -1

Solution:

**(v) 2+2i/1-3i**

**Solution:**

**(vi) 1+7i/(2-i) ^{2}Solution:**

**Question 5.Express the following numbers in the form x + iy:**

**Solution:**

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Solution:

Solution:

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**Question 6.Solution:**

**Question 7.Solution:**

**Question 8.For z = 2 + 3i, verify the following:Solution:**

**Question 9.Solution:**

Solution:

Solution:

Solution: