Question

Ajuda!!! Considerando os seguintes números complexos z1 = 2 + 5i e z2 = 1 + 3i, Determine o valor do PRODUTO e da DIVISÃO deles.

Answer 1

$\mathsf{z_{1}=2+5i}\\\mathsf{z_{2}=1+3i}$

$\mathsf{z_{1}.z_{2}=2+6i+5i+15i^2}\\\mathsf{z_{1}.z_{2}=2+11i-15=-13+11i}$

$\mathsf{\dfrac{z_{1}}{z_{2}}=\dfrac{2+5i}{1+3i}}\\\mathsf{\dfrac{z_{1}}{z_{2}}=\dfrac{(2+5i)(1-3i)}{(1+3i) (1-3i)}}$

$\mathsf{\dfrac{z_{1}}{z_{2}}=\dfrac{2-6i+5i-15i^2}{1^2-{(3i)}^2}}\\\mathsf{\dfrac{z_{1}}{z_{2}}=\dfrac{2-i+15}{1-(-9)}}$

$\mathsf{\dfrac{z_{1}}{z_{2}}=\dfrac{17-i}{10}}$

$\huge \boxed{\boxed{\boxed{\mathsf{\dfrac{z_{1}}{z_{2}}=\dfrac{17}{10}-\dfrac{1}{10}i}}}}$