Question

7. Compute the cube roots of $$z = -8$$. 8. Express each of the following complex numbers in polar form, and plot them in the complex plane, indicating magnitude and angle of each number: $$z = 1 + i\sqrt{3}$$ $$z = 3 + 4i$$ $$z = (\sqrt{3} + i^3)(1 - i)$$ $$z = -5$$ $$z = (1 + i\sqrt{3})^3$$ $$z = -5 - 5i$$ $$z = (1 + i)^5$$ $$z = \frac{1+i\sqrt{3}}{\sqrt{3}+i}$$

Name: 7 compute the cube roots of z 8 8 express each of the following complex numbers in polar form and plot them in the complex plane indicating magnitude and angle of each number z 1 isqrt3 z 3 46359
Uploaded: 2024-02-10T20:33:35-08:00
Duration: 1 min 45 s
Channel: T. L.
Description: 7 compute the cube roots of z 8 8 express each of the following complex numbers in polar form and plot them in the complex plane indicating magnitude and angle of each number z 1 isqrt3 z 3 46359

          7. Compute the cube roots of $$z = -8$$.
8. Express each of the following complex numbers in polar form, and plot them in the complex plane, indicating magnitude and angle of each number:
$$z = 1 + i\sqrt{3}$$
$$z = 3 + 4i$$
$$z = (\sqrt{3} + i^3)(1 - i)$$
$$z = -5$$
$$z = (1 + i\sqrt{3})^3$$
$$z = -5 - 5i$$
$$z = (1 + i)^5$$
$$z = \frac{1+i\sqrt{3}}{\sqrt{3}+i}$$

7 compute the cube roots of z 8 8 express each of the following complex numbers in polar form and plot them in the complex plane indicating magnitude and angle of each number z 1 isqrt3 z 3 46359

Added by Kelsey A.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert T. L.

02/10/2024

Step 1

The magnitude of $$z$$ is $$|z| = |-8| = 8$$. The argument of $$z$$ is $$\theta = \arg(-8) = \pi$$ (since -8 lies on the negative real axis). So, $$z = 8(\cos(\pi) + i\sin(\pi))$$. Show more…

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7. Compute the cube roots of $$z = -8$$. 8. Express each of the following complex numbers in polar form, and plot them in the complex plane, indicating magnitude and angle of each number: $$z = 1 + i\sqrt{3}$$ $$z = 3 + 4i$$ $$z = (\sqrt{3} + i^3)(1 - i)$$ $$z = -5$$ $$z = (1 + i\sqrt{3})^3$$ $$z = -5 - 5i$$ $$z = (1 + i)^5$$ $$z = \frac{1+i\sqrt{3}}{\sqrt{3}+i}$$