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Let $z$ and $w$ be the complex numbers in the picture below:

 If $|z| = 3$ and $|w| = 2$, then what is the real part of $\dfrac{z}{w}$?

 Jan 12, 2019
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im assuming it means pi/3 radians, which is 60 degrees.

 

ok i suck at these, but im gonna give it a try

 

if z=a+bi, a^2+b^2=9

if w=c+di, c^2+d^2=4

 

ignoring the diagram, if w is 2i, then z is -3sqrt3/2+3i/2 by 30-60-90. the quotient is i(-3sqrt3/2+3i/2)/(-2), or (-3/2)/(-2) ignoring the complex part, so the answer is 3/4.

 

 

HOPE THIS HELPED!!!!

 Jan 12, 2019
edited by asdf335  Jan 12, 2019

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