Geometry Problems | MCQs

Explanation

To find the acute angle between the vectors, first find the dot product:

z1 = 3 - 4i

z2 = -4 + 3i

Dot product = (3)(-4) + (-4)(3) = -12 - 12 = -24

Next, find the magnitudes:

|z1| = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5

|z2| = √((-4)^2 + 3^2) = √(16 + 9) = √25 = 5

Now, find the cosine of the angle:

cos(θ) = (Dot product) / (|z1| |z2|)

= -24 / (5 * 5)

= -24 / 25

θ = arccos(-24/25) ≈ 16°16'