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Conjugate of complex numbers and their properties is considered one of the most asked concept.
18 Questions around this concept.
Let be two-zero real numbers. Then the number of elements in the set and is equal to :
The conjugate of a complex number z = a + ib (a, b are real numbers) is a − ib. It is denoted as .
i.e. if z = a + ib, then its conjugate is = a - ib.
Conjugate of complex numbers is obtained by changing the sign of the imaginary part of the complex number. The real part of the number is left unchanged.
Note:
When a complex number is added to its complex conjugate, the result is a real number. i.e. z = a + ib, = a - ib
Then the sum, z + = a + ib + a - ib = 2a (which is real)
When a complex number is multiplied by its complex conjugate, the result is a real number i.e. z = a + ib, = a - ib
Then the product, z・ = (a + ib)・(a - ib) = a2 - (ib)2
= a2 + b2 (which is real)
Geometrically complex conjugate of a complex number is its mirror image with respect to the real axis (x-axis).
For example
z = 2 + 2i and = 2 - 2i
Properties of the conjugate complex numbers:
z, z1, z2, and z3 be the complex numbers
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