Question

Determine o número Z em cada caso:

A) 3z +4i= z-6i20
B) 3i= z+i

Answer 1

$\boxed{\boxed{i^{2}=-1~~~\rightleftharpoons~~~i^{4}=1}}$
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Só isolar z

a)

$3z+4i=z-6i^{20}\\3z-z=-6i^{20}-4i\\2z=-6i^{20}-4i\\2z=2(-3i^{20}-2i)\\z=-3i^{20}-2i\\z=-3i^{4}i^{4}i^{4}i^{4}i^{4}-2i\\z=-3(i^{4})^{5}-2i\\z=-3(-1)^{5}-2i\\z=-3(1)-2i\\\\\boxed{\boxed{z=-3-2i}}$

b)

$3i=z+i\\z+i=3i\\z=3i-i\\z=2i\\\\\boxed{\boxed{z=0+2i}}$