Question

See the attachmnet

Answer 1

@terenzreignz

Answer 2

only part a)

Answer 3

hmm
z and w are complex
|z| = |w| and arg(z) = arg(w)
Let's see.

Answer 4

doesn't this mean that z = w?

Answer 5

but answer is -w

Answer 6

or z = -w

Answer 7

and if it Z=w , then how

Answer 8

or z=-w how

Answer 9

Well, a complex number z has both its modulus |z| and its argument arg(z) right?

Answer 10

yes

Answer 11

If two numbers have the same modulus, then they have the same distance from the the origin 0 + 0i

Answer 12

k

Answer 13

And they have the same angle, too, arg(z) = arg(w)

Answer 14

here arg means argument/amplitude

Answer 15

So, that means, they are collinear.

Answer 16

k

Answer 17

Well, they're like vectors, aren't they?
They'll only be collinear if they're multiples of each other
But their moduli (absolute values) are equal, so they have to be either equal, or negatives of each other :D