6. Prove that:(iii) Vi +、1-1-122

1.	6. Prove that:(iii) Vi +、1-1-122
Answer» i) ((1 + i) / √2)2= (1 + i)2/ 2= (1 + 2i + i2) / 2= (1 + 2i - 1) / 2= 2i / 2= iso√i = (1 + i) / √2 just solve for Z = (√-i) so, z² = -iz is complex and therefore can be represented by x + iy (x+iy)2= -i x2- y2+2xyi = -i xy = -1/2 x2- y2= 0 x = +/-y Therefore (x,y) = (1/sqrt(2),-1/sqrt(2)),(-1/sqrt(2),1/sqrt(2)) And z = 1/sqrt(2)(1-i) = 1/√2(1-i)

Answer»

i) ((1 + i) / √2)2= (1 + i)2/ 2= (1 + 2i + i2) / 2= (1 + 2i - 1) / 2= 2i / 2= iso√i = (1 + i) / √2

just solve for Z = (√-i) so, z² = -iz is complex and therefore can be represented by x + iy

(x+iy)2= -i

x2- y2+2xyi = -i

xy = -1/2

x2- y2= 0

x = +/-y

Therefore (x,y) = (1/sqrt(2),-1/sqrt(2)),(-1/sqrt(2),1/sqrt(2))

And z = 1/sqrt(2)(1-i) = 1/√2(1-i)

Discussion