Question

Find all vectors v in the plane such that ||v||=1 and ||v+i||=1

Answer 1

is this the complex plane ?

Answer 2

no; "i" is a component of a vector on a 2D plane

Answer 3

| v | means v is on the unit circle

Answer 4

||v|| is the magnitude of vector v

Answer 5

yes, and with the tail of v at (0,0) its head must lie on the unit circle

Answer 6

I assume v+i means
\[ v_x \hat{i} + v_y \hat{j} + 1 \hat{i} \]

Answer 7

if so, we can draw this picture