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Maths-

General

Easy

Question

If A= $open square brackets table row i cell negative i end cell row cell negative i end cell i end table close square brackets$ , B = $open square brackets table row 1 cell negative 1 end cell row cell negative 1 end cell 1 end table close square brackets$ , then A⁸ equals

4B
128B
–128B
– 64B

The correct answer is: 128B

we have A = iB
$rightwards double arrow$ A² = (iB)² = i²B² = –B²
= $open square brackets table row 2 cell negative 2 end cell row cell negative 2 end cell 2 end table close square brackets$ = – 2B
$rightwards double arrow$ A⁴ = (–2B)² = 4B² = 4(2B) = 8B
$rightwards double arrow$ A⁸ = (A⁴)² = (8B)² = 64B² = 128B

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