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what is solution to this complex number exponential: (5 - 3i)^7. Any ideas? Give as many forms as possible, i.e., algebraic, exponential, polar...etc. Thank you very much.

 Dec 6, 2015

Best Answer 

 #1
avatar+118723 
+5

 

what is solution to this complex number exponential: (5 - 3i)^7. Any ideas? Give as many forms as possible, i.e., algebraic, exponential, polar...etc.

 

I would start by doing a binomial expansion on it.  Have you done that yet?

 

OR you could just put it straight into the web2 calculator.  

 

(5 - 3i)^7 = -183 640+137 112i

 Dec 6, 2015
 #1
avatar+118723 
+5
Best Answer

 

what is solution to this complex number exponential: (5 - 3i)^7. Any ideas? Give as many forms as possible, i.e., algebraic, exponential, polar...etc.

 

I would start by doing a binomial expansion on it.  Have you done that yet?

 

OR you could just put it straight into the web2 calculator.  

 

(5 - 3i)^7 = -183 640+137 112i

Melody Dec 6, 2015
 #2
avatar
+5

what is solution to this complex number exponential: (5 - 3i)^7. Any ideas? Give as many forms as possible, i.e., algebraic, exponential, polar...etc. Thank you very much.

 

z = (5 - 3i)^7

Algebraic form:
z = -183640+137112i

Exponential form:
z = 229179.733275 × ei 143°15'13″

Trigonometric form:
z = 229179.733275 × (cos 143°15'13″ + i sin 143°15'13″)

Polar form:
r = |z| = 229179.73328
φ = arg z = 143.2537° = 143°15'13″ = 0.79585π
 

 Dec 6, 2015

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