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Question

If a=1+i32,b=1i32 then show that a2=b and b2=a.

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Solution

a=1+i32
a2=(1+i32)2
=1+3i223i4
=132i34
=22i34
=1i32=b
b=1i32
b2=(1i32)2
=1+3i2+23i4
=13+2i34
=2+2i34
=1+i32=a

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