Question

Dados z1 = 10 – 5i e z2 = 2 + 3i, determine . z1/z2

Answer 1

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$\sf{z_1=10-5i~~z_2=2+3i}\\\sf{\dfrac{z_1}{z_2}=\dfrac{10-5i}{2+3i}}\\\sf{\dfrac{z_1}{z_2}=\dfrac{(10-5i)}{(2+3i)}\cdot\dfrac{(2-3i)}{(2-3i)}}\\\sf{\dfrac{z_1}{z_2}=\dfrac{20-30i-10i+15i^2}{2^2-(3i)^2}}\\\sf{\dfrac{z_1}{z_2}=\dfrac{20-40i-15}{4-(-3)}}$

$\sf{\dfrac{z_1}{z_2}=\dfrac{5-40i}{7}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{\dfrac{z_1}{z_2}=\dfrac{5}{7}-\dfrac{40}{7}i}}}}}$