Question

polar form of sqroot3 - sqroot3i

Answer 1

In Cartesian coordinates (x,y)=(√3,-√3).

In polar coordinates, x=rcosθ, y=rsinθ.

x=√3=rcosθ, y=-√3=rsinθ, therefore r²=x²+y²=3+3=6, r=√6.

tanθ=y/x=-1, θ=7π/4 or ¾π. To find out which: x=√3=√6cos(7π/4)=√(6/2), y=-√3=√6sin(7π/4)=-√(6/2). (It's the negative sine component which makes the tangent negative.)

Polar coordinates are (√6,7π/4) or (√6,315°).