Given z is a complex number satisfying $z^{2} - z - | z |^{2} + \frac{64}{| z |^{5}} = 0$ and Re(z) $\neq \frac{1}{2}$ (where Re(z) denotes real part of z), then |z| is less than

Q. If

z

and

w

be two complex numbers such that

| z | \leq 1, | w | \leq 1

and

| z + i w | = | z - i ¯ ¯¯ ¯ w | = 2,

then

Q. If complex numbers

z_{1}

and

z_{2}

both satisfy

z + ¯ z = 2 | z - 1 |

and

arg (z_{1} - z_{2}) = \frac{π}{3},

then find the value of

Im (z_{1} + z_{2})

. (where

Im (z)

denotes the imaginary part of

z

)

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Let P be a point denoting a complex number z on the complex plane. Let Re(z) denotes the real part of z and Im(z) denotes the imaginary part of z. Minimum value of |z| such that |Re(z)|.|Im(z)|=36 is equal to

The correct option is C 6√2 z=|z|(cosA+isin A)Hence|Re(z)|.|Im(z)||z|2(cosAsinA)=|z|22sin2A=36Hence|z|2sin2A=72|z|=6√2√sin2AConsidering A=π4|z|=6√2

Let $P$ be a point denoting a complex number $z$ on the complex plane. Let $R e (z)$ denotes the real part of $z$ and $I m (z)$ denotes the imaginary part of $z$ . Minimum value of $| z |$ such that $| R e (z) | . | I m (z) | = 36$ is equal to