
If then is equal to
A.
B.
C.
D.
Answer
426.6k+ views
Hint: A complex number is of the form where and are real numbers and is an imaginary number. We will use the formula and to solve the given expression. Also, we know that . Here, first we need to multiply by and then, we will make the given expression in the form of and after.
Complete step by step answer:
We need to find the value of the given expression as below,
Multiply the numerator and denominator by , we will get,
We have used brackets so that we can take and (this is an assumption).
We will use the formula and applying in the expression, we get,
We will use the formula and applying it in the expression, we get,
Again we will use the formula and applying it in the expression, we get,
We know that .
Substituting the value of in above expression, we will get,
Removing the brackets, we get,
We are given that .
So, here we will substitute in numerator and in denominator, we will get,
Simplify this above expression, we get,
Dividing by in both numerator and denominator, we get,
Rearrange this above expression, we get,
Dividing by in both numerator and denominator, we get,
Hence, if then is .
Note: Complex Number is an algebraic expression including the factor . These numbers have two parts, one is called the real part and is denoted by Re (z) and the other is called the Imaginary Part called “iota”. Imaginary part is denoted by Im (z) for the complex number represented by 'z'. But either part can be , so all Real Numbers and Imaginary Numbers are also Complex Numbers.
Complete step by step answer:
We need to find the value of the given expression as below,
Multiply the numerator and denominator by
We have used brackets so that we can take
We will use the formula
We will use the formula
Again we will use the formula
We know that
Substituting the value of
Removing the brackets, we get,
We are given that
So, here we will substitute
Simplify this above expression, we get,
Dividing by
Rearrange this above expression, we get,
Dividing by
Hence, if
Note: Complex Number is an algebraic expression including the factor
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