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Question 3 asked for two possible quadrant locations of the product of c + di and , where c, d, e, and f are positive real numbers. The product in question 4 was two complex numbers of the form c + di and , where c, d, e, and f are positive real numbers. You answered the quadrant location of this product.

Provide an example of two complex numbers in the form c + di and , where c, d, e, and f are positive real numbers such that their product lies in the other possible quadrant. Support your example by determining its product.

 May 22, 2020
 #1
avatar+21955 
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I'm not sure what you are asking --

 

In problem 3, are you asking for an example whose product ends in QI and another example whose

product ends in QIV?

If so, (8 + 7i)(6 - 5i)  =  83 + 2i    (QI)

         (3 + 4i)(1 - 2i)  =  11 - 2i     (QIV)

 

In problem 4, are you asking how to solve the problem?

If so:  4sqrt(3) - 4i

          r  =  sqrt( ( 4sqrt(3) )2 + ( -4 )2 )  =  sqrt( 48 + 16 )  =  sqrt( 64 )  =  8

          theta  =  tan-1( -4 / (4sqrt(3) )  =  tan-1( - 1 / sqrt(3) )  =  (-1/6)·pi

          --->     4sqrt(3) - 4i  =  8·cis( (-1/6)·pi )

 

         sqrt(2) + sqrt(2)·i

         r  =  sqrt( ( sqrt(2) )2 + ( sqrt(2) )2 )  =  sqrt( 2 + 2 )  =  sqrt( 4 )  =  2

          theta  =  tan-1( sqrt(2) / sqrt(2) )  =  tan-1( 1 )  =  pi/4

          --->     sqrt(2) + sqrt(2)·i  =  2·cis( pi/4 )

 

Multiplying them together:  8·cis( (-1/6)·pi ) x 2·cis( pi/4 )  =  16·cis( 1/12·pi )

 May 22, 2020
 #2
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question 3 and 4 is done but it mentions them in the question so I included the.  The question is Provide an example of two complex numbers in the form c + di and , where c, d, e, and f are positive real numbers such that their product lies in the other possible quadrant. Support your example by determining its product.

jscare  May 22, 2020

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