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Definition of a Determinant

11 z and w ar...

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11 z and w are non zero complex number and / z / = /w/ and arg( z ) +arg ( w ) = +pie therefore z = , where / / is denoted as modulus

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z

w

be two non-zero complex numbers such that

| z | = | w |

a r g (z) + a r g (w) = π

z

Q. Let z & w be two non zero complex numbers such that

| z | = | w |

A r g z + A r g w = π

, then z equals

z

w

be two non- zero complex numbers such that

| z | = | w |

arg (z) + arg (w) = π

. Then the value of

(z + ¯ ¯¯ ¯ w)^{10}

z

w

be two non- zero complex numbers such that

| z | = | w |

arg (z) + arg (w) = π

. Then the value of

(z + ¯ ¯¯ ¯ w)^{10}

z = 1 + i b = (a, b)

be any complex number,

a, b, ϵ R

\sqrt{- 1} = i .

z \neq 0 + 0 i, a r g z = {tan}^{- 1} (\frac{I m z}{R e z})

- π < a r g z \leq π

a r g (¯ z) + a r g (- z) = {\begin{matrix} π, i f a r g (z) < 0 - π, i f a r g (z) > 0 \end{matrix}

z

w

be non-zero complex numbers such that they have equal modulus values and

a r g z - a r g ¯ w = π,

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