Question

Determine a forma trigonometrica de 7 + 7i

Answer 1

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$\boxed{\sf{\underline{N\acute{u}mero~Complexo~na~forma~trigonom\acute{e}trica}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{Z=\rho\cdot[cos(\theta)+i~sen(\theta)]}}}}}$

$\sf{z=7+7i}\\\sf{\rho=\sqrt{7^2+7^2}=\sqrt{2\cdot7^2}=7\sqrt{2}}\\\sf{sen(\theta)=\dfrac{\diagdown\!\!\!7}{\diagdown\!\!\!7\sqrt{2}}=\dfrac{\sqrt{2}}{2}}\\\sf{cos(\theta)=\dfrac{\diagup\!\!\!7}{\diagup\!\!\!7\sqrt{2}}=\dfrac{\sqrt{2}}{2}}\\\sf{\theta=\dfrac{\pi}{4}}$

$\huge\boxed{\boxed{\boxed{\boxed{\sf{z=7\sqrt{2}\cdot[cos\left(\dfrac{\pi}{4}\right)+i~sen\left(\dfrac{\pi}{4}\right)]}}}}}$