Question
Mathematics Question on Complex Numbers and Quadratic Equations
A man walks a distance of 3 units from the origin towards the North-East (N 45∘ E) direction. From there, he walks a distance of 4 units towards the North-West (N 45∘ W) direction to reach a point P. Then, the position of P in the Arg and plane is
A
3eiπ/4+4i
B
(3−4i)eiπ/4
C
(4+3i)eiπ/4
D
(3+4i)eiπ/4
Answer
(3+4i)eiπ/4
Explanation
Solution
Let OA = 3, so th a t the complex number associated with
A is 3eiπ/4. If z is the complex number associated with P,
then
0−3eiπ/4z−3eiπ/4=34e−iπ/2=−34i
'
⇒3z−9eiπ/4=12ieiπ/4
⇒z=(3+4i)eiπ/4