Converting to Exponential Form

Complex Analysis · Axiom Academy

EXAMPLE Converting to Exponential Form Rewrite the complex number as . Write the complex number in exponential form , where r = |z| is the modulus and is the argument. Nice work. You converted a rectangular complex number to exponential form by finding its modulus and its argument. Modulus: is always non-negative — squaring a = -1 gives (-1)^2 = 1 , so . Quadrant matters: only returns angles in . With and the point sits in Quadrant II, so the true argument is . Modulus tells you how far the number is from the origin; the argument tells you its direction — together they pin down the same point as a + bi .

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