
If then is equal to
A.
B.
C.
D.
Answer
432k+ 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
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

The flightless birds Rhea Kiwi and Emu respectively class 11 biology CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE
