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Question

If m1,m2,m3 and m4 respectively denote the moduli of the complex numbers 1+4i,3+i,1-i and 2-3i, then the correct one, among the following is:


A

m1<m2<m3<m4

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B

m4<m3<m2<m1

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C

m3<m2<m4<m1

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D

m3<m1<m2<m4

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Solution

The correct option is C

m3<m2<m4<m1


Explanation for the correct option:

Modulus of complaex number :

We know that modulus of a complex number z=xi+y is x2+y2

So, the modulus of given complex numbers will be,

m1=1+4i=42+12=17m2=3+i=12+32=10m3=1-i=(-1)2+12=2m4=2-3i=(-3)2+22=13

So, m3<m2<m4<m1

Thus, option (C) m3<m2<m4<m1 is the correct answer.


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