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The complex number  −2+8i has modulus of _____. When  −2+8i is multiplied by 5, the modulus of the product is _____ .

Multiplying a complex number by a real number results in a scalar of the complex number. The quadrant location of the complex number and its product with ______  are the same.

 

Answer choices = 10√17, 5√6, a positive real number, 2√6, the imaginary unit, a complex number, a negative real number, 2√17, √6, 10√6

 Apr 30, 2020
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The modulus of the complex number  a + bi  =  sqrt( a2 + b2 ).

 

For  - 2 + 8i  the modulus is  sqrt( (-2)2 + (8)2 )  =  sqrt( 4 + 64 )  =  sqrt( 68 )  or  3·sqrt( 17 ).

 

If you multiply  -2 + 8I  by  5  you get  5(-2 + 8i)  =  -10 + 40i.

Now, you need to find the modulus of this complex number, place it into reduced radical form, and compare it to the

answer above.

 

To answer in what quadrant you find the original number and the new number, plot both  -2 + 8i  and  -10 + 40i

and answer the question:  Are they in the same quadrant?  If not, what is the location of the second number in

relation to the location of the first number?

 Apr 30, 2020

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