How do you simplify (5-3i)^2?

$16 - 30 i$

Explanation:

Given that

${\left(5 - 3 i\right)}^{2}$

$= \left(5 - 3 i\right) \left(5 - 3 i\right)$

$= 25 - 15 i - 15 i + 9 {i}^{2}$

$= 25 - 30 i - 9$

$= 16 - 30 i$

Jul 28, 2018

color(indigo)(=> 16 - 30 i

Explanation:

${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$, identity.

${\left(5 - 3 i\right)}^{2} = {5}^{2} - \left(2 \cdot 5 \cdot 3 i\right) + {\left(3 i\right)}^{2}$

${i}^{2} = - 1$

$\implies 25 - 30 i - 9$

$\implies 25 - 9 - 30 i$

color(indigo)(=> 16 - 30 i