Question

Given a complex number z = 8, answer the following questions. Show work. A. Find all three distinct cube roots of z. Label the three roots z1, z2, z3. Express all the roots in both trigonometric and standard form. Give exact value. B. Then graph each root in the complex plane. Clearly label the roots including the modulus value of the roots.

Name: given a complex number z 8 answer the following questions show work a find all three distinct cube roots of z label the three roots z1 z2 z3 express all the roots in both trigonometric and s 79002
Uploaded: 2022-01-10T14:09:03-08:00
Duration: 4 min 47 s
Channel: Syed Basim Mehmood
Description: given a complex number z 8 answer the following questions show work a find all three distinct cube roots of z label the three roots z1 z2 z3 express all the roots in both trigonometric and s 79002

          Given a complex number z = 8, answer the following
questions. Show work.
A.  Find all three distinct cube roots
of z. Label the three
roots z1, z2, z3. Express
all the roots in both trigonometric and standard form. Give exact
value.
B.  Then graph each root in the complex
plane. Clearly label the roots including the modulus value of the
roots.

Added by Felicia L.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Syed Basim Mehmood

01/10/2022

Step 1

Since \(z = 8 = 8 + 0i\), the modulus of \(z\) is \(|z| = \sqrt{8^2 + 0^2} = 8\) and the argument of \(z\) is \(\theta = \text{atan2}(0, 8) = 0\). Show more…

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Given a complex number z = 8, answer the following questions. Show work. A. Find all three distinct cube roots of z. Label the three roots z1, z2, z3. Express all the roots in both trigonometric and standard form. Give exact value. B. Then graph each root in the complex plane. Clearly label the roots including the modulus value of the roots.