Class 11 Math Chapter 1 Exercise 1.2 Notes (New Book 2026) Click Here To Download Ex : 1.1 Ex : 1.3 Ex : 1.4 Ex : 1.5 MCQs 📝 Exercise 1.2 – Complete Explanation (Question by Question) Question 1 In this question, we have to find the real values of x and y. We are given an equation where complex numbers are on both sides. When two complex numbers are equal, their real parts are equal and their imaginary parts are equal. First, we simplify the equation. Then we compare the real parts and the imaginary parts separately. This gives us two simple equations. We solve those equations and get the values of x and y. Question 2 Here, the value of z is given and we also have z written as x + yi. We are given one more equation: z – 2z = –27 + 15i. We put the value of z into this equation. Then we simplify. After simplifying, we compare the real parts and the imaginary parts. This gives us the values of x and y. It is a simple linear equation. Question 3 This question has three different parts. In each part, we have (x + iy) whole square given, and on the other side there is a complex number. First, we expand (x + iy)² using the formula (a + b)² = a² + 2ab + b². But here b is iy, so iy whole square becomes –y². So we get x² – y² + 2ixy. Then we compare the real part of this with the real part of the given complex number. And we compare the imaginary part with the imaginary part. This gives us two equations. We solve them to find x and y. Question 4 In this question, z1 and z2 are given. z1 = 2 + 3i and z2 = –1 – ai. We have to find the real value of a. The condition given is that the imaginary part of z1 multiplied by z2 is equal to 7. So first we multiply z1 and z2. After multiplication, we look at the imaginary part of the answer. We set that imaginary part equal to 7. Then we solve the equation and find the value of a. Question 5 Here we have two complex numbers: z1 = x + yi and z2 = a + bi. We have to find the values of x, y, a, and b. Two conditions are given. First: z1 + z2 = 10 + 4i. Second: z1 – z2 = 6 + 2i. From the first condition, we get equations for x + a and y + b. From the second condition, we get equations for x – a and y – b. Then we solve these four equations together and find the values of x, y, a, and b. Question 6 In this question, we have to prove a property of complex numbers. It is about the modulus of complex numbers. We are given two complex numbers z1 and z2. We have to show that some relation between their moduli is true. We simply apply the formula for modulus and simplify. The answer comes out directly. It is a straightforward proof. Question 7 Here we have to find the square root of complex numbers. There are four parts. For each complex number, we need to find its square root. The method is the same for all. We assume that the square root of (x + iy) is a + ib. Then we square both sides. Then we compare the real parts and the imaginary parts. This gives us two equations. We solve these equations to find a and b. That gives us the square root. Question 8 In this question, we have to find the square root of 13 – 20√3i. We use the same method as in question 7. We assume the square root is a + ib, square both sides, and compare real and imaginary parts. After finding the square root in the form a + ib, we have to represent it on an Argand diagram. That means we plot the point (a, b) on a graph. The x-axis is the real part and the y-axis is the imaginary part. Question 9 Here we are given an equation that has complex numbers. We have to find the real values of x and y. First, we simplify the equation. We multiply the complex numbers where needed. Then we add or subtract as given. After simplifying, we compare the left-hand side with the right-hand side. Real parts are equated to real parts. Imaginary parts are equated to imaginary parts. Then we solve the two simple equations to find x and y. Question 10 This question is similar to question 9. We have an equation with x and y. We simplify the equation first. Then we compare the real part and the imaginary part with the right-hand side. This gives us two equations. We solve them to find x and y. Question 11 In this question, we have to find the real values of u and v. The equation has a fraction with complex numbers. First, we simplify the fraction. To simplify, we multiply the numerator and denominator by the conjugate of the denominator. Then we compare the result with 4i. The real part should be 0 and the imaginary part should be 4. From this, we get equations and solve for u and v. Question 12 Here, z1 = 4 + 5i and z2 = a – 2i are given. We have to find the real value of a. The condition is that the real part of z1 multiplied by z2 is equal to 20. First, we multiply z1 and z2. Then we look at the real part of the answer. We set that real part equal to 20. Then we solve the equation and find the value of a. Leave a Reply Cancel reply Logged in as mubasharaliraza121@gmail.com. Edit your profile. Log out?

Class 11 Math Chapter 1 Exercise 1.1 Notes (New Book 2026) Click Here To Download Ex : 1.2 Ex : 1.3 Ex : 1.4 Ex : 1.5 MCQs Who Every Question Work ( Exercise : 1.1 ) In the first question of Exercise 1.1, we have to find the multiplicative inverse, there are 2 ways for that, we write the complex number in 2 ways like (a, b) or a+b, if we want to find the inverse, we write it in the form of a+b and write it as 1 / a+b which is its multiplicative inverse, after that we rationalize it, that is, we multiply and divide by changing the sign of the lower value, and solve it.  In the 2nd method, we use the formula, the first value is a, the 2nd value is b, we find the value by applying it in the formula. In the 2nd question, we have to solve the answer and write the real and imaginary part, by doing that we rationalize and the question gets solved in a simple way. In the 3rd question, we prove that z bar = z, if z is real, then we have to convert z = a + b to real, then it will be proved, we assume that z bar = z and the value of b is 0 and put it in the equation containing z, then z = a remains, then we take the bar and again z is obtained and it gets proved. In the 4th question we have to prove b, in the 1st part we have to divide z+z times by 2 to get the answer real no of z, i.e. if z = a+ib then by solving we get the answer “a” and it is proved. In the 5th part the values ​​of z1, z2, z3 are given, we have to solve and write the answer a+b, in solving we have to multiply z1 times by z2 times and divide it by z3, then rationalize and solve. In the 6th part we give the values ​​of z1, z2 which are applied in the question then take the determinant or mart and it gets solved.  7 I have to prove that if n is a factor of 1 then we get a common line, like if n is a factor of 1 then we get -1 inside where i is squared. 8 I have to solve by rationalizing and then finding the least value of n. 9 I have to prove that if n is a factor of 1 then we get that if n is a factor of 1 then we get n = 4q + r and we will solve. Main Topics Are :  Complex number  recognition of real and legendary parts  conjugate of complex number  operations on complex number  complex number as ordered there of real numbers  properties of the fundamental operations are complex number Argand diagram Leave a Reply Cancel reply Logged in as mubasharaliraza121@gmail.com. Edit your profile. Log out? Required fields are marked * Message*