simplify (s+4-7i)^2

Solution

simplify

(s + 4 - 7 i)^{2}

(s^{2} + 8 s - 33) + (- 56 - 14 s) i

Solution steps

(s + 4 - 7 i)^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(s + 4 - 7 i)^{2} = (s + 4 - 7 i) (s + 4 - 7 i)

= (s + 4 - 7 i) (s + 4 - 7 i)

Distribute parentheses

= ss + s \cdot 4 + s (- 7 i) + 4 s + 4 \cdot 4 + 4 (- 7 i) - 7 i s - 7 i 4 - 7 i (- 7 i)

Simplify

ss + s \cdot 4 + s (- 7 i) + 4 s + 4 \cdot 4 + 4 (- 7 i) - 7 i s - 7 i 4 - 7 i (- 7 i) : - 56 i + s^{2} + 8 s - 14 s i - 33

= - 56 i + s^{2} + 8 s - 14 s i - 33

Rewrite in standard complex form:

(s^{2} + 8 s - 33) + (- 56 - 14 s) i

= (s^{2} + 8 s - 33) + (- 56 - 14 s) i

\frac{1}{( 7 - 5 \cdot i \cdot x ) ^{7}}

(x + Δ x)^{2} - 2 (x + Δ x) + 2

- \frac{2}{10} (1 - 2 x + 2)

\frac{p g sin ( θ ) ( - y ^{2} + 2 L ^{2} y )}{2 L m}

\frac{x ^{2} + 2 s + 53}{( s ^{2} + 49 ) \cdot ( s + 2 )}