# Problems from Complex numbers from polar to binomic form

Write in binomic form $$13_{120^{\circ}}$$.

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### Development:

To convert a complex number in polar form into binomial form, we must calculate the coefficients of the real part and the imaginary part of the number. By means of the formula proposed:

$$a=13\cdot\cos(120^{\circ})=13\cdot\Big(-\dfrac{1}{2}\Big) = -\dfrac{13}{2}$$

$$b=13\cdot\sin(120^{\circ})=13\cdot\Big(\dfrac{\sqrt{3}}{3}\Big) = \dfrac{13\cdot\sqrt{3}}{3}$$

This way, $$13_{120^{\circ}}= -\dfrac{13}{2} + \dfrac{13\cdot\sqrt{3}}{3} i$$\$

### Solution:

$$13_{120^{\circ}}= -\dfrac{13}{2} + \dfrac{13\cdot\sqrt{3}}{3} i$$

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