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Question

If z1=5+12i and |z2|=4, then

A
maximum (|z1+iz2|)= 17
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B
maximum (|z1+(1+i)z2)=13+42
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C
minimum ∣ ∣z1z2+4z2∣ ∣=134
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D
minimum ∣ ∣z1z2+4z2∣ ∣=135
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Solution

The correct options are
A maximum (|z1+iz2|)= 17
B maximum (|z1+(1+i)z2)=13+42
D minimum ∣ ∣z1z2+4z2∣ ∣=135
z1=5+12i&|z2|=4
|z1+iz2||z1|+|iz2||z1+iz2||5+12i|+|i||z2||z1+iz2|13+4maximum(|z1+iz2|)=17
|z1+(1+i)z2||z1|+|(1+i)z2||z1+(1+i)z2||5+12i|+|i+1||z2||z1+iz2|13+42maximum(|z1+(1+i)z2|)=13+42
z2z1+4z1z2z2z1+4z1z2z2z1+4z1z24|12+5i|+44|12+5i|=413+113z2z1+4z1z2513∣ ∣ ∣ ∣z1z2+4z2∣ ∣ ∣ ∣135minimum⎜ ⎜ ⎜∣ ∣ ∣ ∣z1z2+4z2∣ ∣ ∣ ∣⎟ ⎟ ⎟=135
Hence, options 'A', 'B' and 'D' are correct.

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