
If then ?
Answer
500.4k+ views
Hint: Complex numbers are numbers of the form axis b where ‘a’ is the real part of the complex number and ‘b’ is the imaginary part of the complex number. In complex number
The multiplication of a complex number and its conjugate is formulated as:
be the complex number and its conjugate is
Complete step-by- step solution:
Given
We know,
Proof: On multiplying, we get:
On cancelling and , we get:
Substituting , we get:
On using equation (2) in equation(1) we have
Now we have to find the value of:
Substituting from (3) in (4), we have:
By taking LCM, we get:
We know,
On cancelling , we get
Hence the required value is:
Note: Every complex number has associated with it another complex number known as its complex conjugate. You find the complex conjugate simply by changing the sign of the imaginary part of the complex number. Example: To find the complex conjugate of we change the sign of the imaginary part. Thus, the complex conjugate of is . We have multiplied a complex number by its conjugate and the answer is a real number. This is a very important property which applies to every complex conjugate pair of numbers.
In conjugate of a complex number only the imaginary part of that complex number changes its sign.
The multiplication of a complex number and its conjugate is formulated as:
Complete step-by- step solution:
Given
We know,
Proof: On multiplying, we get:
On cancelling
Substituting
On using equation (2) in equation(1) we have
Now we have to find the value of:
Substituting
By taking LCM, we get:
We know,
On cancelling
Hence the required value is:
Note: Every complex number has associated with it another complex number known as its complex conjugate. You find the complex conjugate simply by changing the sign of the imaginary part of the complex number. Example: To find the complex conjugate of
In conjugate of a complex number only the imaginary part of that complex number changes its sign.
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