Question

Alguém poderia me ajudar a achar o módulo deste número complexo 3i/1+i

Answer 1

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$\rm{Vamos~escrever~o~n\acute{u}mero~na~forma~z=a+bi}\\\sf{z=\dfrac{3i}{1+i}}\\\sf{\dfrac{3i}{(1+i)}\cdot\dfrac{(1-i)}{(1-i)}}\\\sf{\dfrac{3i-3i^2}{1^2-i^2}}\\\sf{\dfrac{3i-3\cdot(-1)}{1-(-1)}}\\\sf{\dfrac{3i+3}{1+1}}\\\sf{z=\dfrac{3}{2}+\dfrac{3}{2}i}\\\sf{\rho=\sqrt{\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^2}}\\\sf{\rho=\sqrt{\dfrac{9}{4}+\dfrac{9}{4}}}\\\sf{\rho=\sqrt{2\cdot\dfrac{9}{4}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{\rho=\dfrac{3\sqrt{2}}{2}}}}}}$