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Question
State whether the following statement is true or false.(1−2i)3+i+(2−3i)3−i=i
State whether the following statement is true or false.
(1−2i)3+i+(2−3i)3−i=i
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Solution
The correct option is B False
Taking LHS:
(1−2i)3+i+(2−3i)3−i
=(1−2i)(3−i)+(2−3i)(3+i)(3+i)(3−i)
=1−7i+9−7i10
=10−14i10
And RHS=1Hence LHS is not equal to RHS. So above satement is false.
Taking LHS:
(1−2i)3+i+(2−3i)3−i
=(1−2i)(3−i)+(2−3i)(3+i)(3+i)(3−i)
=1−7i+9−7i10
=10−14i10
And RHS=1
Hence LHS is not equal to RHS. So above satement is false.
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