The correct options are
A Maximum value of |z1+iz2| is 17
B Minimum value of |z1+(1+i)z2| is 13−4√2
D Maximum value of ∣∣
∣
∣
∣∣z1z2+4z2∣∣
∣
∣
∣∣ is 133
Here, |z1+iz2|≤|z1|+|iz2|≤13+4≤17
|z1+(1+i)z2|≥||z1|−|(1+i)z2||≥13−4√2
Now, ∣∣∣|z2|−4|z2|∣∣∣≤∣∣∣z2+4z2∣∣∣≤|z2|+4|z2|
⇒3≤∣∣∣z2+4z2∣∣∣≤5
∵|z1|=13
∴∣∣
∣
∣
∣∣z1z2+4z2∣∣
∣
∣
∣∣ has minimum value as 135 and maximum value as 133