let = z = -6 + 13i (rectangular form x + yi)

You want to express it polar form

i.e z = r(cos θ + i sin θ)

r = |z| = √(x² + y²)

= √((-6)² + 13²)

= √(36 + 169)

= √205

tan θ = y/x = -13/6

basic θ = tan-¹(-13/6) ≈ -65.22° (2 d.p)

But -6 + 13i has a negative real component and a positive imaginary component. This means it lies in the top left portion of the axes (second quadrant)

So arg z = 180° - 65.22° = 114.78°

Therefore,

-6 + 13i = √205(cos 114.78° + i sin 114.78°)

≈ 14.32(cos 114.78° + i sin 114.78°)

The other way to express it is :

14.32 ∠ 114.78°

La la la la la

Shut the Fuchs up