Cho số phức z thỏa mãn |z-1-i|=1. Khi 3|z|

Đáp án B

Đặt z=a+bi⇒z−1−i=1⇔a−12+b−12=1⇔a2+b2=2a+2b−1.

Khi đó3z+2z−4−4i=3a2+b2+2a−42+b−42=32a+2b−1+2a2+b2−8a−8b+32=32a+2b−1+22a+2b−1−8a−8b+32=32a+2b−1+2−6a−6b+31=36a+6b−3+2−6a−6b+31≤32+226a+6b−3−6a−6b+31=14

Dấu “=” xảy ra khia2+b2=2a+2b−16a+6b−33=−6a−6b+312⇔a+b=52a2+b2=4⇒z=a2+b2=2