
If , then the value of the expression is
(a)-1
(b)1
(c)2
(d)None of these
Answer
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Hint: In this question, we can use the concept of power of Iota. Iota is square root of minus 1 means . For example, what is the value of Iota's power 3? Iota so is and hence .
Complete step-by-step answer:
It is given that and let us consider the given expression, put in the given expression.
First work out on the expansion by using
Second work out on the expansion by using
Third work out on the expansion by using
Now put all the values in the equation (1), we get
Rearranging the terms, we get
Collecting all constant terms and iota terms, we get
Finally, we get
Hence the value of the given expression is 1 and which is purely real number.
Therefore, the correct option for the given question is option (b).
Note: We might get confused by the word purely imaginary. A complex number is said to be purely imaginary if it has no real part. For example, 3i, i, 5i, and −12i are all examples of pure imaginary numbers, or numbers of the form bi, where b is a nonzero real number.
Complete step-by-step answer:
It is given that
First work out on the expansion
Second work out on the expansion
Third work out on the expansion
Now put all the values in the equation (1), we get
Rearranging the terms, we get
Collecting all constant terms and iota terms, we get
Finally, we get
Hence the value of the given expression
Therefore, the correct option for the given question is option (b).
Note: We might get confused by the word purely imaginary. A complex number is said to be purely imaginary if it has no real part. For example, 3i, i, 5i,
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