dumpIing
Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

[tex]z^{7}=128i[/tex]

z = ____ + ____ i

Sagot :

LammettHash

If z ⁷ = 128i, then there are 7 complex numbers z that satisfy this equation.

[tex]z^7 = 128i = 2^7i = 2^7e^{i\frac\pi2}[/tex]

[tex]\implies z=\sqrt[7]{2^7} e^{i\frac17\left(\frac\pi2+2n\pi\right)}[/tex]

(where n = 0, 1, 2, …, 6)

[tex]\implies z = 2 e^{i\left(\frac\pi{14}+\frac{2n\pi}7\right)}[/tex]

[tex]\displaystyle\implies z = 2 \left(\cos\left(\frac\pi{14}+\frac{2n\pi}7\right)+i\sin\left(\frac\pi{14}+\frac{2n\pi}7\right)\right)[/tex]

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.