simplify (-3+5i)^2

Solution

simplify

(- 3 + 5 i)^{2}

- 16 - 30 i

Solution steps

(- 3 + 5 i)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Simplify

(- 3)^{2} + 2 (- 3) \cdot 5 i + (5 i)^{2} : - 30 i - 16

= - 30 i - 16

Rewrite in standard complex form:

- 16 - 30 i

= - 16 - 30 i

\frac{4 ^{2}}{4 ^{6}}

- 4 x^{2} - 3 x - 3 + (- 4) x^{2} - 9 x

∣ - 2 - 5 ∣

\frac{4 c ^{5}}{4 ( c ) ^{3}}

\frac{4 + 5}{2 + 5}