Final answer:
The quotient of the given complex numbers is 1/3(cos90° + isin90°), which simplifies to 1/3i.
Step-by-step explanation:
The quotient of two complex numbers is found by dividing their magnitudes and subtracting their angles when they are in polar form. The division of 3(cos135° + isin135°) by 9(cos45° + isin45°) can be simplified by dividing their magnitudes (3/9 = 1/3) and subtracting their angles (135° - 45° = 90°). This calculation results in a new complex number in polar form: 1/3(cos90° + isin90°).
Given that cos90° is 0 and sin90° is 1, we can rewrite this expression as 1/3(0 + i*1), which simplifies to 1/3i. Therefore, the quotient of the given complex numbers is 1/3i.