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1.6bFree

Two ways to give the same directions

Your guide: Sir AhmedSays brackets have saved more marks than any calculator.

The problem

So far you've described a point by walking east then north: go 1 block across, then √3 blocks up. But you could just as easily say: walk 2 blocks, turned 60° from straight ahead. Same spot, different instructions.

This second way of giving directions is the polar form. It needs only two numbers: how far (the modulus r, which you already know) and which way (a new number called the argument).

The polar form of z = x + iy is z = r(cosθ + isinθ). Here r = |z| = √(x² + y²) is the modulus. θ = tan⁻¹(y/x) is the argument — the angle z makes with the positive real axis.

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