Question

(1-i)²-(1+I)²/(1-i)³+(1+i)³

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Answer 1

Answer:

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Step-by-step explanation:

How do I simplify the expression (1-i)³-(1+i)³/(1-i)²-(1+i)²?

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(1-i)^3-(1+i)^3/(1-i)^2-(1+i)^2

=[(1-i)^5+(1+i)^3-(1-i^2)^2]/(1-2i+i^2)

=(1-5i+10i^2-10i^3+5i^4-i^5+1+3i+3i^2+i^3–4)/-2i

=(1-5i-10+10i+5-i+1+3i-3-i-4)/-2i

=(1-10+5+1-3-4-5i+10i-i-i+3i)/-2i

=(6i-10)/-2i

=(5/i)-3

=-(5i+3) otherwise if the function is like [(1-i)^3-(1+i)^3]/[(1-i)^2-(1+i)^2] then

=[(1-i-1-i)^3+3(1-i)(1+i)(1-i-1-i)]/[(1-i+1+i)(1-i-1-i)]

=[(-2i)^3+3(-2i)(1-i^2)]/2×(-2i)

=[8i+(-i)6×2]÷(-4i)

=[8i-12i]÷(-4i)

=-4i/-4i

=1