Question 29852
{{{ (2+3i)^3 }}} Write the quantity 3 times as denoted by the exponent
{{{ highlight ((2+3i)(2+3i))(2+3i) }}} foil the first two quantities
F : 2 * 2 = 4
O : 2 * 3i = 6i
I : 2 * 3i = 6i
L : 3i * 3i = 9i^2 = 9(-1) = -9
{{{ 4 + 6i + 6i -9  }}}
{{{ (-5 + 12i) }}} now foil this with the 3rd quantity from the start of the problem
{{{ (-5 + 12i)(2 + 3i) }}}
F : -5 * 2 = -10
O : -5 * 3i = -15i
I : 12i * 2 = 24i
L : 12i * 3i = 36i^2 = 36(-1) = -36
{{{ -10 - 15i + 24i - 36 }}} combine like terms
{{{ -46 - 9i }}}