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
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