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Given ab=21-20i  and |b|=29 , find |a|

 

Much help appreciated!!!!!

 Nov 4, 2019
 #1
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"Given ab=21-20i  and |b|=29 , find |a|"

 

Let     \(a=u+iv\text{ , }b=x+iy\)

 

Then   \(ab=ux-vy+i(vx+uy)\)

 

so     \(ux-vy=21\\vx+uy=-20\)

 

Solve these equations to find u and v in terms of x and y.

 

Then, make use of    \(|b|=\sqrt{x^2+y^2}=29\\\)   to find \(|a|=\sqrt{u^2+v^2}\)

 

(You should find |a| = 1).

 Nov 4, 2019
 #2
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|a|.|b| = | 21 - 20i | = sqrt(21^2 + 20^2) = sqrt(441 + 400) =sqrt(841).

|b| = 29 = sqrt(841), so |a| = 1.

Guest Nov 4, 2019
 #3
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thank you!!!

 Nov 4, 2019

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