Proving z1.(z2.z3) = (z1.z2).z3 using the associative law/property?

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Let

z1 = (x1, y1)

z2 = (x2, y2)

z3 = (x3, y3)

how do you prove that z1(z2z3) = (z1z2)z3 using the associative law?

Is it possible to just compute for the right side?

I saw this answer

(z1 z2) z3 = (x1 x2 - y1 y2 + i (x1y2+x2y1))(x3+iy3) =

=x3x1x2-x3y1y2-x1y2y3-x2y1y3 + i (x1x2y3-y1y2y3+x1y2x3+x2y1y3)

z1 (z2z3) = (x1 + 1y1) (x2x3-y2y3 + i (x2y3+x3y2)) =

= x1x2x3 - x1y2y3 - x2y3y1 - y1x3y2 + i (x1x2y3+x1x3y2+y1x2x3-y1y2y3)

but it really doesnt make sense to me and id like to solve this without using " i "

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