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    IBMediumNumber10–12

    Dividing Two Complex Numbers in Polar Form

    Dividir Dois Números Complexos na Forma Polar

    Let z1=4(cos⁡π3+isin⁡π3)z_{1} = 4\left(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}\right) and z2=2(cos⁡π4+isin⁡π4)z_{2} = 2\left(\cos\frac{\pi}{4} + i\sin\frac{\pi}{4}\right). Find z1z2\frac{z_{1}}{z_{2}} in polar form.

    In polar form a division acts on the two parts of a complex number in two different ways. Decide what happens to the moduli and what happens to the arguments before touching the numbers.

    Solution

    Step 1 of 5

    1. 1.Dividing in polar form divides the moduli and subtracts the arguments: