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Properties of Conjugate of a Complex Number

If π5 and ...

Question

If $\frac{π}{5}$ and $\frac{π}{3}$ are respectively the arguments of ${¯ ¯ ¯ z}_{1}$ and $z_{2}$ , what is the value of $(a r g z_{1} + a r g z_{2})$ ?

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Solution

arguments of $_{1} = π / 5$
then, arguments of $z_{2} = \frac{- π}{5}$
and arguments of $z_{2} = \frac{π}{3}$
$∴$ arguments $z_{1}$ + arguments $z_{2} = \frac{- π}{5} + \frac{π}{3} = \frac{2}{15} π$

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Similar questions

| z_{1} - z_{2} | = | z_{1} | + | z_{2} |

, then prove that

a r g (z_{1}) - a r g (z_{2}) = π

z_{1}, z_{2}

are complex numbers then the correct match List- I to List II is:

List - I	List - II
A) arg z_1z_2	1) $a r g z_{1} - a r g z_{2}$
B) $a r g z_{1}_{2}$	2) $a r g z_{1} - a r g z_{2} = \frac{π}{2}$
C) $\| z_{1} + z_{2} \| = \| z_{1} - z_{2} \|$	3) $a r g z_{1} = a r g z_{2}$
D) $\| z_{1} + z_{2} \|^{2}$	4) $a r g z_{1} + a r g z_{2}$
E) $\| z_{1} + z_{2} \| = \| z_{1} \| + \| z_{2} \|$	5) $r_{1}^{2} + r_{2}^{2} + 2 r_{1} r_{2} c o s (θ_{1} - θ_{2})$

\frac{π}{3}

\frac{π}{4}

are the arguments of

z_{1}

_{2}

, then the value of arg

(z_{1} . z_{2})

z_{1}

z_{2}

are two complex numbers such that

| z_{1} | = | z_{2} |

a r g z_{1} + a r g z_{2} = π

z_{1}

z_{2}

a r g z_{1} = \frac{π}{2}

a r g {¯ ¯ ¯ z}_{2} = \frac{π}{4}

a r g (\frac{z_{1}}{z_{2}}) =

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