Complex numbers (1 Viewer)

[imsleepyz]

Please help me! I don't know where to start...

 

[gurmies]

Note that OA + OP = OB. OP = OB - OA = 9+8i - (3+5i) = 6 + 3i.

OQ = iOP = i(6+3i) = -3 + 6i.

 

[imsleepyz]

Thanks gurmies. But why is OA + OP = OB?

 

[imsleepyz]

Oh, I get it! It's a vector sum! Thanks gurmies!

 

[Carrotsticks]

Any two vectors in R2 pointing in the same direction that are equal in magnitude AND parallel are equal.

They said AB and OP have the same length (this means equal in magnitude)

They also said AB is parallel to OP.

Therefore vector AB = vector OP.

But vector AB = B - A = 6+3i.

But OP = P - O = 6+3i

But O = 0 + 0i (it's the origin), so therefore P = 6+3i.

To get Q, we rotate vector OP by 90 degrees ie: multiply by cis(90), which is the same thing as multiplying by i.

So therefore to get OQ, it's just i x OP = -3+6i.

 

[imsleepyz]

Ahhh thanks for making it clearer. Thanks Carrotsticks!