How do you simplify i6(2i−i2−3i3)?

2 Answers
Areej J. · F. Javier B.
Mar 12, 2018

The answer is -1-5i

Explanation:

First we factorize powers of i.So i6 would become -1. 3i3 would become -3i and i2 would become -1.By putting values
−1(2i−(−1)+3i). Now −1(2i+3i+1) would become −1(5i+1) and then −5i−1
I HOPE IT HELPS:)

F. Javier B.
Mar 12, 2018

See details below

Explanation:

Expand expresion.

i6(2i−i2−3i3)=2i7−i8−3i9

But we know that:

i1=i
i2=−1 (by definition)
i3=i2⋅i=−i
i4=i2⋅i2=(−1)⋅(−1)=1
i5=i4⋅i=1⋅i=i and starts again
i6=i5⋅i=i⋅i=i2=−1
i7=i6⋅i=−i

for this cliclic result, we can write:

i6(2i−i2−3i3)=2i7−i8−3i9=−2i−1−3i=−1−5i

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