If 5z2/11z1is purely imaginary, then the value of |(2z1+3z2)/(2z1-3z2)|is
Finding the value of |(2z1+3z2)/(2z1-3z2)|:
Given that 5z2/11z1 is purely imaginary
Let us take 5z2/11z1=iy
z2/z1=11iy/5|(2z1+3z2)/(2z1-3z2)=z1(2+3z2/z1)/z1(2-3z2/z1)=(2+3(11iy/5))/(2-3(11iy/3))(2z1+3z2)/(2z1-3z2)=(10+33iy)/(10-33iy)|(2z1+3z2)/(2z1-3z2)|=(100+1089)/(100+1089)=1
Hence, the value of |(2z1+3z2)/(2z1-3z2)| is 1.
if z1 and z2 are complex numbers
5z2 / 11z1 is purely imaginary then find the mode of 2z1+3z2 / 2z1-3z2