Let p, q and r be three unequal numbers such that p, q and r are in AP. If \( (q - p) \), \( (r - q) \) and p are in GP, then \( (p + q) : (q + r) : (r + p) \) equals
If p, \( g_{1} \), \( g_{2} \) and q are in GP and m is the arithmetic mean of p and q, then \( \frac{g_{1}^{2}}{g_{2}} + \frac{g_{2}^{2}}{g_{1}} \) is equal to
Consider the following inequalities:
I. \( 1 + 4i > 3 + 2i \)
II. \( 2 + 3i < 3 + 4i \)
III. \( 4 + 3i > 3 + 4i \)
where \( i = \sqrt{-1} \)
How many of the above are valid?
Let \( Z_{1} \) and \( Z_{2} \) be complex numbers such that \( \frac{3Z_{1}}{4Z_{2}} \) is purely imaginary. What is \( \left|\frac{Z_{1} + Z_{2}}{Z_{1} - Z_{2}}\right| \) equal to?
