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What you mean?
e^z1*e^z2=e^z1+z2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Sum and product of roots
[src]
/ z1\
| z1 - e | z1
- W\-e / - e
$$\left(- e^{z_{1}} - W\left(- e^{z_{1} - e^{z_{1}}}\right)\right)$$
/ z1\
| z1 - e | z1
- W\-e / - e
$$- e^{z_{1}} - W\left(- e^{z_{1} - e^{z_{1}}}\right)$$
/ z1\
| z1 - e | z1
- W\-e / - e
$$\left(- e^{z_{1}} - W\left(- e^{z_{1} - e^{z_{1}}}\right)\right)$$
/ z1\
| z1 - e | z1
- W\-e / - e
$$- e^{z_{1}} - W\left(- e^{z_{1} - e^{z_{1}}}\right)$$
/ z1\
| z1 - e | z1
z2_1 = - W\-e / - e
$$z_{2 1} = - e^{z_{1}} - W\left(- e^{z_{1} - e^{z_{1}}}\right)$$