The correct options are
A maximum (|z1+iz2|)= 17
B maximum (|z1+(1+i)z2)=13+4√2
D minimum ∣∣
∣∣z1z2+4z2∣∣
∣∣=135
z1=5+12i&|z2|=4
|z1+iz2|≤|z1|+|iz2|⇒|z1+iz2|≤|5+12i|+|i||z2|⇒|z1+iz2|≤13+4∴maximum(|z1+iz2|)=17
|z1+(1+i)z2|≤|z1|+|(1+i)z2|⇒|z1+(1+i)z2|≤|5+12i|+|i+1||z2|⇒|z1+iz2|≤13+4√2∴maximum(|z1+(1+i)z2|)=13+4√2
∣∣∣z2z1+4z1z2∣∣∣≤∣∣∣z2z1∣∣∣+∣∣∣4z1z2∣∣∣⇒∣∣∣z2z1+4z1z2∣∣∣≤4|12+5i|+44|12+5i|=413+113⇒∣∣∣z2z1+4z1z2∣∣∣≤513⇒∣∣
∣
∣
∣∣z1z2+4z2∣∣
∣
∣
∣∣≥135∴minimum⎛⎜
⎜
⎜⎝∣∣
∣
∣
∣∣z1z2+4z2∣∣
∣
∣
∣∣⎞⎟
⎟
⎟⎠=135
Hence, options 'A', 'B' and 'D' are correct.