6 Write each of the following complex numbers in the form a + bi. (a)* 3 cis120°
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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![**Problem 6:** Write each of the following complex numbers in the form \(a + bi\).
**(a)** \(3 \, \text{cis} \, 120^\circ\)
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This problem asks to convert a complex number given in polar form to its equivalent in rectangular form. The polar form \( r \, \text{cis} \, \theta \) can be expressed as:
\[ r \cdot (\cos \theta + i \sin \theta) \]
So, to convert \(3 \, \text{cis} \, 120^\circ\) to the form \(a + bi\), compute:
\[ a = 3 \cdot \cos 120^\circ \]
\[ b = 3 \cdot \sin 120^\circ \]
Thus, \(3 \, \text{cis} \, 120^\circ = 3(\cos 120^\circ + i \sin 120^\circ)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffce2c460-26f0-4070-86e1-b1876f7380a8%2F8f5c4f08-44e9-4f95-a4df-3efacdefba87%2Frv6wnma_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 6:** Write each of the following complex numbers in the form \(a + bi\).
**(a)** \(3 \, \text{cis} \, 120^\circ\)
---
This problem asks to convert a complex number given in polar form to its equivalent in rectangular form. The polar form \( r \, \text{cis} \, \theta \) can be expressed as:
\[ r \cdot (\cos \theta + i \sin \theta) \]
So, to convert \(3 \, \text{cis} \, 120^\circ\) to the form \(a + bi\), compute:
\[ a = 3 \cdot \cos 120^\circ \]
\[ b = 3 \cdot \sin 120^\circ \]
Thus, \(3 \, \text{cis} \, 120^\circ = 3(\cos 120^\circ + i \sin 120^\circ)\).
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