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/sci/ - Science & Math

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2864998 No.2864998 [Reply] [Original]

How would you find the solutions to this?

|z-1-i| >= 4

(z: a+bi)

>> No.2865012

|z - (1 + i)| >= 4
|z - a| >= 4

means the distance between z and a is greater than, or equal to, 4 units. In this case, a is (1+i)
So z is 4 or more units away from (1+i), making it all points outside and on the circle around (1+i) with radius 4

>> No.2865015
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2865015

>>2865012
true true

>> No.2865055

you could just make the 4 negative when solving the modulus instead of the first side to make it easier

>> No.2865087

like this?
http://www.wolframalpha.com/input/?i=|%28x%2Biy%29-1-i|%3E%3D4

>> No.2865224

or this?
http://www.wolframalpha.com/input/?i=|z-1-i|%3E%3D4