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Given the following complex number, find the following.

 

3√2 + 6i^87

 

a) Simplify the complex number to not include any large exponents.  

 

 

b) Find the modulus.  

 

any pointers would be appreicated 

 May 12, 2020

Best Answer 

 #1
avatar+25786 
+2

I will assume this is  6 (i^87)  

     rememeber this:             i^2 = -1         i^3 = -i           i^4 = 1  

  

6 (i^87)    =  6  (i^4)21 * i^3     = 6* 1* -i  =   -6i   

3 sqrt 2  - 6i

 

modulus = sqrt of both parts squared and added

 

sqrt(  (3 sqrt2)^2  +  (-6i)^2)

     sqrt( 18 + -36(-1) ) =  sqrt 54

 May 12, 2020
edited by ElectricPavlov  May 13, 2020
 #1
avatar+25786 
+2
Best Answer

I will assume this is  6 (i^87)  

     rememeber this:             i^2 = -1         i^3 = -i           i^4 = 1  

  

6 (i^87)    =  6  (i^4)21 * i^3     = 6* 1* -i  =   -6i   

3 sqrt 2  - 6i

 

modulus = sqrt of both parts squared and added

 

sqrt(  (3 sqrt2)^2  +  (-6i)^2)

     sqrt( 18 + -36(-1) ) =  sqrt 54

ElectricPavlov May 12, 2020
edited by ElectricPavlov  May 13, 2020

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