Question

Express the following complex number in the standard form (¹⁄₃ + 3i)³
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Answer 1

Correct question :

Express the following complex number in the standard form a + ib (¹⁄₃ + 3i)³

Answer :

→ $( 1/3 + 3i )^3\:=\:( 1/3 )^3 + ( 3i )^3 + 3( 1/3 ) ( 3i ) ( 1/3 + 3i )$

→ $1/27 + ( 27i^3) + 3i ( 1/3 + 3i )$

→ $1/27 + 27 ( -i ) + i + 9i^2$$[i^3 = -i ]$

→ $1/27 - 27 + i - 9$ $[i^2 = -1 ]$

→ $[ 1 / 27 - 9 ] + i ( -27 + 1 )$

→ $-242 / 27 - 26i$

Form :

→ $a + ib$

→ $a\:=\:-242/27$

→ $b\:=\:-26$

♥ So, It's Done ♥ !!