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bleakarcher

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If you solve (pi/4)+x=2pi you get 7pi/4 not 3pi/4 (PS sorry for annoying you for so long)
 

Carrotsticks

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math man,

You seriously need a tablet.

Kind regards,

My eyes.

Edit: and my neatness OCD.
 

SpiralFlex

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@You guys

Up at 1:08 AM doing maths on Valentines Day....
 

math man

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Math has various limits,
Obviously we are infinite limits
That work at all hours
 

math man

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I just really want to get this through my mind.
The reasoning is not so striaght forward but bear with me. Now arg(z-5i)=-theta and arg(z+5i) = phi. subbing this into locus gives phi + theta = pi/4. however this
statement is only true in the sense of subtracting the arguments of the vectors. Whereas in plane geometry it is obvious that both phi and theta are obtuse so adding them
together will become a reflex angle so you add 180 to pi/4 which gives 5pi/4 and then you subtract this from 2pi which gives the desired angle of 3pi/4. If you dont get this
then im sorry, but yeh dw most complex locus questions of this form are not as complicated as i am putting it. Basically if the vectors are subtended from the y-axis then
if the locus is in form arg[(z-z1)(z-z2)]= theta, then the angle between the vectors will be (theta + pi/2) and i don't think you have to prove it every time unless they ask you to
 

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