Want to know if there is a better way to...

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Want to know if there is a better way to go about this problem.

Something nags at me that expanding the squares after squaring both sides is unnecessarily tedious.

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>>7775203

if you write y= (1+i)z = sqrt(2)*exp(i*pi/4)*z,

then y describes the circle of center 2 and of radius 4

which means z describes the circle of center 2 and of radius 2sqrt(2)

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>>7775217

also maybe I'm just saying shit so be careful.

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>>7775203

You definitely want to isolate the z so maybe do (1+i)z-2=(1+i)(z-(1-i))?

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>>7775223

Well, your radius is fine but the center seems off.

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>>7775229

ok I don't understand why the first method is false, but you can do the same thing |z - 2/(1+i)| = 2sqrt(2) -> circle of radius 2sqrt(2) centered around 1-i

but I don't know why the first one doesn't work

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>>7775236

Well, you don't really explain what you're doing. You write it up right and then conclude that it's centered around 2.

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>>7775245

You have to be kidding

|y-2| = r is the circle of center 2 and radius r.

Ok so I found the mistake in

>>7775217

the set of points described by y is indeed the circle of center 2 and radius 4

to obtain z though, you have to take this set and multiply it by (1-i)/2 (since z = (1-i)y/2)

so this will rotate the circle around the origin (including the center).

In the end, you indeed find the center (1-i)*2/2 = (1-i) and the radius 2sqrt(2)

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