Question

para os numeros complexos z1=2+4i e z2=1+3i Calcule: a) z1.z2 b)z2/z1

Answer 1

Olá.

$\mathbf{Lembretes:}\\\\ \boxed{\mathsf{z_1=2+4i}}\ \boxed{\mathsf{z_2=1+3i}}\\ \\\begin{array}{ccc}i^0&=&1\\i^1&=&i\\i^2&=&-1\\i^3&=&-i}\end{array} \\\\\\ \mathsf{z_1\cdot z_2=}\mathsf{(2+4i)\cdot(1+3i)=}\\\mathsf{2+6i+4i+12i^2=}\\\mathsf{2+10i+12\cdot(-1)=}\\\mathsf{2+10i-12=}\\\boxed{\mathsf{-10+10i}}\\\\\\\mathsf{\dfrac{z_2}{z_1}=\dfrac{1+3i}{2+4i}=}\\\\\mathsf{\dfrac{1+3i}{2+4i}\cdot\dfrac{2-4i}{2-4i}=}\\\\\mathsf{ \dfrac{2-4i+6i-12i^2}{4-8i+8i-16i^2}=}$

$\mathsf{\dfrac{2+2i-12\cdot(-1)}{4-16\cdot(-1)}}=\\\\\mathsf{\dfrac{2+2i+12}{4+16}=}\\\\\mathsf{\dfrac{14+2i}{20}=}\\\\\\\mathsf{\left(\dfrac{14+2i}{20}\right)^{:2}=\boxed{\mathsf{\dfrac{7+i}{10}}}}$

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Bons estudos.