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.

jscare May 22, 2020

#1**0 **

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 )

geno3141 May 22, 2020

#2**0 **

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