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Number of ordered pairs (s), (a,b) of re...

Number of ordered pairs `(s)`, `(a,b)` of real numbers such that `(a+ib)^(2008)=a-ib` holds good is

A

`2008`

B

`2009`

C

`2010`

D

`1`

Text Solution

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The correct Answer is:
C
`(c )` Let `z=a+ib`
`implies barz=a-ib`
Hence, we have `z^(2008)=barz`
`:. |z|^(2008)=|barz|=|z|`
`:. |z|[|z|^(2007)-1]=0`
`:. |z|=0` or `|z|=1`,
If `|z|=0impliesz=0`
If `|z|=1z^(2009)=zbarz=|z|^(2)=1`
`implies2009` values of `z`
`implies` Toal `=2010`
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