complex no. prob (1 Viewer)

[AGB]

gday everyone....can someone please explain the deduce part of this question to me...

1. Find the modulus and arguement of each of the complex numbers z and w, where:

z = (1 + i) / (1 - i)

w = (sqrt2) / (1 - i)

Plot the points representing z,w and z + w on an Argand diagram (I can do this bit). Deduce from the diagram that

tan (3*pi)/8 = (sqrt2) + 1 (i cant do this bit )

thanks

 

[nike33]

cant draw diagram..

let z+w = point a
o = origion

angle (zoa) = B
angle (aow) = B
angle (owx) = pi/4


angle (zoa) + angle (aow) + angle(owx) = pi/2
2B + pi/4 = pi/2
B = pi/8

The arg of z+w is

angle (aox) = angle (aow) + angle(wox) = 3pi/8

and angle (aox) = arg(z+w) = 3pi / 8 *

then

z + w = sqr(2)/2 +i(sqr(2)+2)/2

tan@ = ((sqr(2) +2)/2) / (sqr(2)/2)
tan@ = sqr(2) + 1

hence tan (3pi / 8) = sqr(2) + 1 (from *)


i hope this is right..