Complex NumbersHard
Question
A man walks a distance of 3 units from the origin towards the north-east (N45o E) direction. From there, he walks a distance of 4 units towards the north-west (N 45o W) direction to reach a point P. Then the position of P in the Argand plane is
Options
A.3eiπ/4 + 4i
B.(3 - 4i)eiπ/4
C.(4 + 3i)eiπ/4
D.(3 + 4i)eiπ/4
Solution
Let OA = 3, so that the complex number
associated with A is 3eiπ/4
If z is the complex number associated with P,
then
e-iπ/2 = - 
⇒ 3z - 9eiπ/4 = 12ieiπ/4
⇒ z = (3 + 4i)eiπ/4.
associated with A is 3eiπ/4
If z is the complex number associated with P,
then
e-iπ/2 = - ⇒ 3z - 9eiπ/4 = 12ieiπ/4
⇒ z = (3 + 4i)eiπ/4.
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