SOLUTION: If z1 and z2 are complex numbers and |z2| = 4 , |z1|+ i×|z2|= 3 + 4i , then value of |z2 + i × z1|=... [ 9, 16, 5 , 25 ]

Question 1208271: If z1 and z2 are complex numbers and |z2| = 4 , |z1|+ i×|z2|= 3 + 4i , then value of |z2 + i × z1|=...
[ 9, 16, 5 , 25 ]
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
.
If z1 and z2 are complex numbers and |z2| = 4 , |z1|+ i×|z2|= 3 + 4i , then value of |z2 + i × z1|=...
[ 9, 16, 5 , 25 ]
~~~~~~~~~~~~~~~~~~~~~~~~~~

Read the problem attentively.  It says that  |z1|+ i×|z2| = 3 + 4i.


This means that  |z1| = 3,  |z2| = 4.


Now, due to the "triangle" inequality for adding complex number, 
the general rule is that for all complex numbers z1 and z2

    |z2 + z1| <= |z2| + |z1|.


Hence, in your case,  |z2 + i*z1|  can not be greater than 4 + 3 = 7.


Thus, options  9, 16, 25 do not work.


The only acceptable option is the remaining value of 5.

Solved, with complete explanations.

This problem is a Math joke on complex numbers.

RELATED QUESTIONS
z1 and z2 are two complex numbers. if |z1+z2|=|z1|+|z2| then show that... (answered by venugopalramana)

If z1 , z2 are two complex numbers , |z1|=|z2| , and Arg(z1 + z2) = pi/4 ,find... (answered by ikleyn)

If z1 and z2 are two complex numbers with |z1|=|z2| ,then which of the following are... (answered by Edwin McCravy,Fombitz)

Let z1 and z2 be two complex numbers such that |z1| = 5 and z1/z2 + z2/z1 = 0. Find |z1... (answered by CPhill,ikleyn)

for all complex no. z1, z2 satisfying modz1=12 and mod(z2-3-4i),the minimum value of... (answered by richard1234)

given that z1=2+i and z2=-3+4i and 1/z3=1/z1+1/z2. determine the value of z3 in standard... (answered by mananth,Edwin McCravy,math_tutor2020)

the modulus or absolute value of a complex numbers: if z2=4+3i and z2=-2+3i (answered by stanbon)

z1=2+i z2=-3+i... (answered by Edwin McCravy)

hi z1=1-3i/4+5i , z2=3-4i/5-6i z1/z2 ? thnx alot (answered by ewatrrr,MathLover1)