simplify (5+4i)^2

Solution

simplify

(5 + 4 i)^{2}

9 + 40 i

Solution steps

(5 + 4 i)^{2}

Apply Perfect Square Formula:

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

(5 + 4 i)^{2} = 5^{2} + 2 \cdot 5 \cdot 4 i + (4 i)^{2}

= 5^{2} + 2 \cdot 5 \cdot 4 i + (4 i)^{2}

Simplify

5^{2} + 2 \cdot 5 \cdot 4 i + (4 i)^{2} : 40 i + 9

= 40 i + 9

Rewrite in standard complex form:

9 + 40 i

= 9 + 40 i

\frac{3}{2} x^{2} + \frac{4}{3} x - \frac{7}{3} x^{2} + \frac{5}{2} x

(+ \frac{3}{5}) - (+ \frac{10}{5}) + (+ \frac{9}{5}) - (- \frac{3}{5})

\frac{m ^{2} - 11 m + 30}{m - 6}

- 4 x - 10 x

(x - 7)^{2}