Grade 12Algebra
If z1 z2 are two non real complex numbers Z1+z2 and z1z2 are real numbers then z1=
If z1 z2 are two non real complex numbers Z1+z2 and z1z2 are real numbers then z1=
2 Answers
Vikas TU
Dear student
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Good Luck
Aditya Gupta
this ques is very easy.
let z1= x1 + iy1
and z2= x2 + iy2
then z1+z2= (x1+x2) + i(y1+y2)
which is real when y1+y2= 0 or y2= – y1
also, z1*z2= (x1 + iy1)(x2 – iy1)
= x1x2 – ix1y1 + iy1x2 + y1^2
= x1x2+y1^2 + iy1(x2 – x1)
which is real when y1(x2 – x1)= 0
obviously y1 cannot be 0 as z1 and z2 are non reals.
so, (x2 – x1)= 0
or x1= x2
so, z1= x1 + iy1
and z2= x1 – iy1
so that z1 = conjugate (z2).
so, z1 and z2 are conjugate pairs of each other.
kindly approve :=))
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