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Question Number 154429 by liberty last updated on 18/Sep/21

Commented by liberty last updated on 18/Sep/21

$$$$$$A=\sqrt[3]{-15+\frac{28\sqrt{3}i}{9}}+\sqrt[3]{-15-\frac{28\sqrt{3}i}{9}}$$$$$$

Commented by EDWIN88 last updated on 18/Sep/21

$$abs(-15\pm \frac{28\sqrt{3}}{9}i)=\frac{19\sqrt{57}}{9}\approx 15.9385$$$$arg(-15+\frac{28\sqrt{3}}{9})=\arctan \left(\frac{28\sqrt{3}}{135}\right)\approx 19.7603°$$$$arg(-15-\frac{28\sqrt{3}i}{9})=-\arctan \left(\frac{28\sqrt{3}}{135}\right)\approx -19.7603°$$$$abs\left(\sqrt[3]{-15\pm \frac{28\sqrt{3}i}{89}}\right)=\sqrt[3]{abs(-15\pm \frac{28\sqrt{3}}{9})}\approx 2.5166$$$$arg\left(\sqrt[3]{-15+\frac{28\sqrt{3}i}{9}}\right)=\frac{1}{3}arg(-15+\frac{28\sqrt{3}i}{9})\approx 6.5867°$$$$arg\left(\sqrt[3]{-15-\frac{28\sqrt{3}i}{9}}\right)=\frac{1}{3}arg(-15-\frac{28\sqrt{3}i}{9})\approx -6.5867°$$$$\iff \sqrt[3]{-15+\frac{28\sqrt{3}i}{9}}=1.5+2i$$$$$$$$\iff \sqrt[3]{-15-\frac{28\sqrt{3}i}{9}}=1.5-2i$$$$\iff A=3$$

Commented by liberty last updated on 18/Sep/21

$$theanswerA=3$$

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