If Z= 5+12i then |Z|=
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Answered by
1
Step-by-step explanation:
z
1
=5+12i,∣z
2
∣=4
∣z
1
+iz
2
∣≤∣z
1
∣+∣z
2
∣=13+4=17
∴∣z
1
+(1+i)z
2
∣≥∣∣z
1
∣−∣1+i∣∣z
2
∣∣
=13−4
2
∴min(∣z
1
+(1+i)z
2
∣)=13−4
2
∣
∣
∣
∣
∣
z
2
+
z
2
4
∣
∣
∣
∣
∣
≤∣z
2
∣+
∣z
2
∣
4
=4+1=5
∣
∣
∣
∣
∣
z
2
+
z
2
4
∣
∣
∣
∣
∣
≥∣z
2
∣−
∣z
2
∣
4
=4−1=3
∴max
∣
∣
∣
∣
∣
∣
z
2
+
z
2
4
z
1
∣
∣
∣
∣
∣
∣
=
3
13
andmin
∣
∣
∣
∣
∣
∣
z
2
+
z
2
4
z
1
∣
∣
∣
∣
∣
∣
=
5
13
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