Answer:
Z1/Z2 is (8/13) + (6/13)i.
Explanation:
To evaluate Z1/Z2, we need to divide the complex number Z1 by the complex number Z2.
To do this, we can use the formula for dividing complex numbers:
(Z1/Z2) = (Z1 * (conjugate of Z2)) / (Z2 * (conjugate of Z2))
where the conjugate of a complex number is obtained by changing the sign of the imaginary part.
Using this formula, we have:
Z1/Z2 = (4-2i) / (2+3i)
We multiply both the numerator and denominator by the conjugate of Z2, which is (2-3i), to eliminate the imaginary part from the denominator:
Z1/Z2 = (4-2i) / (2+3i) * (2-3i) / (2-3i)
Expanding the numerator and denominator, we get:
Z1/Z2 = [(42) + (43i) - (23i) - (29i^2)] / [(22) + (23i) - (3i2) - (3i3i)]
Simplifying the terms, we get:
Z1/Z2 = (8 + 6i) / (4 + 9)
Z1/Z2 = (8 + 6i) / 13
Therefore, Z1/Z2 is (8/13) + (6/13)i.