easy complex number question but i just cant do it!! :'( (1 Viewer)

[coeyz]

anyone can helpp??
thankssssssss!!!!!!!

 

[coeyz]

i cant do the second question

 

[andy.sanders]

this might help

cos90+isin90=i

 

[Iruka]

Grown-ups use radians.

I think you mean cos (pi/2) + i sin(pi/2) = i

 

[coeyz]

ye i know anticlockwise 90 degrees is times i ..

but the problem is,
i cant get the vector of z4 - z1

 

[Trebla]

z₄ - z₁ is the vector P₁P₄

 

[andy.sanders]

Grown-ups use radians.

I think you mean cos (pi/2) + i sin(pi/2) = i

hahaha ye but i didnt know how to put it in radians on the computer

 

[Iruka]

Yes, but if you don't put in the degrees sign then it already is in radians.

 

[jet]

Part i) Vector P₂P₁=Vector P₄P₁ rotated by (pi)/2

Therefore z₂ - z₁ = i(z₄ - z₁)

Part ii) Therefore 1 + 5i - z₁ = i(5 + 3i - z₁)
1 + 5i - z₁ = -3 + 5i - iz₁
(-1 + i)z₁ = -4
z₁ = -4/(-1 + i)
(some steps in the middle)
= 2 + 2i
Also, P₃P₁ = P₂P₁ + P₄P₁
Therefore z₃ - z₁ = z₂ - z₁ + z₄-z₁
z₃ - (2 + 2i) = (1 + 5i) - (2 + 2i) + (5 + 3i) - (2 + 2i)
z₃= (1 + 5i) + (5 + 3i) - (2 + 2i)
z₃ = 4 + 6i

 

[coeyz]

Thanks A Lot!!!!!!!!!

 

[jet]

You're welcome