z= (cos 315 + i sin 315) Write each complex number in standard form.?

Question

I need to understand what steps you took to arrive at the answer. Any help is much appreciated. Thanks in advance you Trig geniuses.

Answer 1

z= (cos 315 + i sin 315)
=(1/sqrt2) - (1/sqrt2)i
=0.707 - 0.707i (approx)

cos(315) = cos(315-360)
= cos(-45)
= cos(45)
= 1/sqrt(2)

sin(315) = sin(315-360)
= sin(-45)
= -sin(45)
= -1/sqrt(2)

Answer 2

315° = - 45°
cos 315° = cos (- 45°) = cos 45° = 1/√2
sin 315° = sin(- 45°) = - sin 45° = - 1 / √2
z = 1/√2 - i (1/√2)
z = (1/√2).(1 - i)

Answer 3

z= (cos 315 + i sin 315)
z= sqrt2/2 + -sqrt2/2 i

or if you need it in polar form

r= sqrt(a² +b²)
r=sqrt(1/2 + 1/2)
r=1

theta=arctan(b/a)
=arctan((-sqrt2/2)/(sqrt2/2))
=arctan(-1)
=-pi/4

z=(1,pi/4)