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Suppose m = 2 + 6i, and | m + n | = 3√10, where n is a complex number.

 

a) what is the minimum value of the modulus of n?

b) provide one example of the complex number, n.

 Apr 20, 2022

Best Answer 

 #1
avatar+488 
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Modulus just means the length of the complex number from zero.

The values of  | m + n | = 3√10 would sit on a circle with radius 3√10

The best way to reach that radius whilst minimizing the length is to draw a straight line. That is if you represent m and n as vectors, they would have the same direction. 

This could be proven to be the minimum length by using theorems like the law of cosines or triangle inequality.

To illustrate my point, move around n and try to find the minimum length of the black line:

https://www.desmos.com/calculator/7kyjosrdcu

 Apr 21, 2022
 #1
avatar+488 
+2
Best Answer

Modulus just means the length of the complex number from zero.

The values of  | m + n | = 3√10 would sit on a circle with radius 3√10

The best way to reach that radius whilst minimizing the length is to draw a straight line. That is if you represent m and n as vectors, they would have the same direction. 

This could be proven to be the minimum length by using theorems like the law of cosines or triangle inequality.

To illustrate my point, move around n and try to find the minimum length of the black line:

https://www.desmos.com/calculator/7kyjosrdcu

textot Apr 21, 2022

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