Can you help me with steps please?

Question

1022 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-28T03:34:23

$z = 5 e^{i \frac{π}{3}} = 5 \sqrt[3]{- 1}$ $z=5e^(ipi/3)=5root(3)(-1)$

.

$z = 5 e^{i \frac{π}{3}}$ $z=5e^(ipi/3)$

$z = 5 e^{\frac{i π}{3}}$ $z=5e^((ipi)/3)$

Rule of complex numbers:

$e^{i a π} = {(- 1)}^{a}$ $e^(iapi)=(-1)^a$

Here, $a = \frac{1}{3}$ $a=1/3$ . Therefore:

$e^{i (\frac{1}{3}) π} = {(- 1)}^{\frac{1}{3}} = \sqrt[3]{- 1}$ $e^(i(1/3)pi)=(-1)^(1/3)=root(3)(-1)$

$z = 5 e^{i \frac{π}{3}} = 5 \sqrt[3]{- 1}$ $z=5e^(ipi/3)=5root(3)(-1)$