Simply complex!

Algebra Level 4

If the equation zz12+zz22=k|z-z_{1}|^{2}+|z-z_{2}|^{2}=k represents the equation of a circle, where z1=2+3iz_{1}=2+3i and z2=4+3iz_{2}=4+3i are the extremities of a diameter, then the value of kk is:

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