If A 2 + 3 i and B 3 + 4 i are two vertices of a square A B C D (taken in anticlockwise order) in a complex plane, then the value of Z 3 2 - Z 4 2 (where C is Z 3 and D is Z 4 ) is equal to

Step-by-step solution

Z 4 - 2 + 3 i 3 + 4 i - 2 + 3 i = e i π / 2 = i ⇒ Z 4 = 2 + 3 i + i - 1 = 1 + 4 i and Z 3 - 3 + 4 i 2 + 3 i - 3 + 4 i = e - i π / 2 = - i ⇒ Z 3 = 3 + 4 i + i - 1 = 2 + 5 i ⇒ Z 3 2 - Z 4 2 = 29 - 17 = 1 2