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Complex Numbers question

2019 · 10 Jan · Shift 1 · Q37

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JEE Main
Mathematics
Complex Numbers
2019 · 10 Jan · Shift 1 · Q37

Complex Numbers question

2019 · 10 Jan · Shift 1 · Q37

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let z1 and z2 be any two non-zero complex numbers such that

3\left| {{z_1}} \right| = 4\left| {{z_2}} \right|.

If

z = {{3{z_1}} \over {2{z_2}}} + {{2{z_2}} \over {3{z_1}}}

then :

A
${\rm I}m\left( z \right) = 0$
B
$\left| z \right| = \sqrt {{17 \over 2}}$
C
$\left| z \right| =$ ${1 \over 2}\sqrt {9 + 16{{\cos }^2}\theta }$
D
Re(z) $=$ 0

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