If $z$ is a complex number such that $z = -\overline{z}$,then $z$:

  • A
    $z$ is purely real
  • B
    $z$ is purely imaginary
  • C
    $z$ is any complex number
  • D
    real part of $z$ is the same as its imaginary part

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Let $z_1$ and $z_2$ be two complex numbers such that $z_1 + z_2$ and $z_1 z_2$ are both real. Then:

The multiplicative inverse of the complex number $(\sin \theta, \cos \theta)$ is

If $\bar{z}$ is the conjugate of the complex number $z$,then which of the following relations is false?

Let $Z_1$ and $Z_2$ be any two complex numbers.
Statement $1: |Z_1 - Z_2| \ge |Z_1| - |Z_2|$
Statement $2: |Z_1 + Z_2| \le |Z_1| + |Z_2|$

If $z = r{e^{i\theta }},$ then $|{e^{iz}}| = $

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