Question: Show that each complex nth root of a nonzero complex number w has the same magnitude.Question content area bottomPart 1What formula gives the nth roots

Show that each complex nth root of a nonzero complex number w has the same magnitude.Question content area bottomPart 1What formula gives the nth roots of a complex number wequalsr left parenthesis cosine theta 0 plus i sine theta 0 right parenthesis? Let wnot equals0, ngreater than or equals2 be an integer, and kequals0,1,2,..., nminus1.A.z Subscript k equals r Superscript n Baseline left bracket cosine left parenthesis k theta 0 right parenthesis plus i sine left parenthesis k theta 0 right parenthesis right bracketz Subscript kequalsr Superscript n Baseline left bracket cosine left parenthesis k theta 0 right parenthesis plus i sine left parenthesis k theta 0 right parenthesis right bracketB.z Subscript k equals RootIndex n StartRoot r EndRoot left bracket cosine left parenthesis k theta 0 right parenthesis plus i sine left parenthesis k theta 0 right parenthesis right bracketz Subscript kequalsRootIndex n StartRoot r EndRoot left bracket cosine left parenthesis k theta 0 right parenthesis plus i sine left parenthesis k theta 0 right parenthesis right bracketC.z Subscript k equals RootIndex n StartRoot r EndRoot left bracket cosine left parenthesis StartFraction theta 0 Over n EndFraction plus StartFraction k pi Over n EndFraction right parenthesis plus i sine left parenthesis StartFraction theta 0 Over n EndFraction plus StartFraction k pi Over n EndFraction right parenthesis right bracketz Subscript kequalsRootIndex n StartRoot r EndRoot left bracket cosine left parenthesis StartFraction theta 0 Over n EndFraction plus StartFraction k pi Over n EndFraction right parenthesis plus i sine left parenthesis StartFraction theta 0 Over n EndFraction plus StartFraction k pi Over n EndFraction right parenthesis right bracketD.z Subscript k equals RootIndex n StartRoot r EndRoot left bracket cosine left parenthesis StartFraction theta 0 Over n EndFraction plus StartFraction 2 k pi Over n EndFraction right parenthesis plus i sine left parenthesis StartFraction theta 0 Over n EndFraction plus StartFraction 2 k pi Over n EndFraction right parenthesis right bracketz Subscript kequalsRootIndex n StartRoot r EndRoot left bracket cosine left parenthesis StartFraction theta 0 Over n EndFraction plus StartFraction 2 k pi Over n EndFraction right parenthesis plus i sine left parenthesis StartFraction theta 0 Over n EndFraction plus StartFraction 2 k pi Over n EndFraction right parenthesis right bracket

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