Question

. Find modulus and conjugate of the complex no. + ​

Answer 1

Answer:Complex numbers are represented in a binomial form as (a + ib). It almost invites you to play with that ‘+’ sign. What happens if we change it to a negative sign? Let z = a + ib be a complex number. We define another complex number  ¯ z  such that  ¯ z  = a – ib. We call  ¯ z

or the complex number obtained by changing the sign of the imaginary part (positive to negative or vice versa), as the conjugate of z. Let us now find the product  z ¯ z  = (a + ib)×(a – ib)

Hence,  z ¯ z  = {a2 -i(ab) + i(ab) + b2 } = (a2 + b2 )   …(1)

If a and b are large numbers, the sum in (1) will be greater. So one can use this equation to measure the value of a complex number.

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