If z1 and z2 are -5 and -3 respectively- then find z1 - z2

Fact: #160; Arg(z)+Arg (z)=0 So Arg(z_1)= π5 , also given Arg(z_2)=π3 Hence #160; Arg(z_1)+Arg (z_2)= π5+π3=2π15 ...

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Nth Term of a GP

If z1 and ...

Question

If $arg (_{1})$ and $arg (z_{2})$ are $\frac{π}{5}$ and $\frac{π}{3}$ respectively, then find $(arg z_{1} + arg z_{2})$

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Solution

Fact: $Arg (z) + Arg (¯ ¯ ¯ z) = 0$

So $Arg (z_{1}) = - \frac{π}{5}$ , also given $Arg (z_{2}) = \frac{π}{3}$

Hence $Arg (z_{1}) + Arg (z_{2}) = - \frac{π}{5} + \frac{π}{3} = \frac{2 π}{15}$

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If arg(¯¯¯¯¯z1) and arg(z2) are π5 and π3 respectively, then find (argz1+argz2)

Fact: Arg(z)+Arg(¯¯¯z)=0So Arg(z1)=−π5, also given Arg(z2)=π3Hence Arg(z1)+Arg(z2)=−π5+π3=2π15

If $arg (_{1})$ and $arg (z_{2})$ are $\frac{π}{5}$ and $\frac{π}{3}$ respectively, then find $(arg z_{1} + arg z_{2})$

Fact: $Arg (z) + Arg (¯ ¯ ¯ z) = 0$

So $Arg (z_{1}) = - \frac{π}{5}$ , also given $Arg (z_{2}) = \frac{π}{3}$

Hence $Arg (z_{1}) + Arg (z_{2}) = - \frac{π}{5} + \frac{π}{3} = \frac{2 π}{15}$