Question

w = 2+4i
It is given that p is a real number such that 0.25pi <= arg(w+p)<=0.75pi. Find the set of possible values of p

Answer 1

@ganeshie8

Answer 2

@Luigi0210 @mathstudent55

Answer 3

@Directrix

Answer 4

@Preetha @Photon336

Answer 5

@jabez177

Answer 6

@inkyvoyd @ShadowLegendX

Answer 7

@Data_LG2

Answer 8

@ireallydontlikemath @jabez177 @Luigi0210 @Mehek14 @MissSmartiez @phi @purple_pink @retirEEd @surjithayer @YoungStudier

Answer 9

I would first find the angle of w
can you do that ?

Answer 10

yes

Answer 11

but you cant do that since p is being added to the real part of the complex number

Answer 12

so arg(w+p) cannot equal to arg w +arg p

Answer 13

if we make a sketch, it looks like this