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>> Algebraic Operations on Complex Numbers Part-1
Algebraic Operations on Complex Numbers
Fundamental Operations with complex numbers:
In performing operations with complex numbers we can proceed as in the algebra of real numbers replacing i2 by -1 when it occurs.
(a+bi) + (c+di) = (a+c)i + (b+d)i
(a+bi) - (c+di) = (a-c)i + (b-d)i
(a+bi)(c+di) = ac+bc i+ bi2
= (ac+bd+(bc-ad)i)/(c2-d2i2 )
=(ac+bd)/(c2+d2 )+(bc-ad)/(c2+d2) i
Inequalities in imaginary numbers are not defined. There is no validity if we say that imaginary is positive or negative.
GC: z >0, 4 + zi < 2+4i are meaningless.
In real numbers if a2 + b2=0 then a=b=0; however in complex numbers,
z12 + z22 does not imply z1 = z2 = 0
Equality in complex numbers
Two complex numbers z1 = a1 + ib, and z2 = a2 + ib2 are equal if their real and imaginary parts are equal.
i.e. z1 = z2 = Rs(z1) = Re(z1)
and Im(z1) = Im (z2).