Question

Find the complex number that satisfies \(|z-2i|=2,arg(z+2)<\frac{\pi}{4}\)

Answer 1

my solution:
\[\arg(z+2)=\frac{\pi}{4}\implies z+2=a+ai\implies z=a-2+ai\]
\[|z-2i|=2\implies (a-2)^2+(a-2)^2=4\implies a=2+\sqrt2\]
answer
\[z=2+(2+\sqrt2)i\]
@phi

Answer 2

yes , that's good

Answer 3

\[\color\magenta\heartsuit\]

Answer 4

@phi @misty1212 what section would this fall under for me too review? Complex numbers?