1.

If the number of ordered pairs `(a,b)` where `a,b in R` such that `(a+ib)^(5015)=(a-ib)^(3)` is `k`, then the unit digit of `k` is equal to________

Answer» Correct Answer - 9
`a+ib=zimplies|z|^(5015)-|z|^(3)=0`
`|z|^(3)(|z|^(5012)-1)=0`
`|z|=0` or `|z|^(5012)=1implies|z|implieszbarz=1`
`z=0`
`z^(5015)=barz^(3)=z^(5015)=1/(z^(3))impliesz^(5018)=1`
Number of complex numbers `=5018+1=5019`


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