simplify (5-4zi)^2

Solution

simplify

(5 - 4 z i)^{2}

(25 - 16 z^{2}) - 40 z i

Solution steps

(5 - 4 z i)^{2}

Apply Perfect Square Formula:

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

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

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

5^{2} = 25

- 2 \cdot 5 \cdot 4 z i = - 40 z i

(4 z i)^{2} = - 16 z^{2}

= 25 - 40 z i - 16 z^{2}

Rewrite in standard complex form:

(25 - 16 z^{2}) - 40 z i

= (25 - 16 z^{2}) - 40 z i

C (- 4, 1) yD (3, - 5)

\frac{64 ( s + 10 ) ( s + 50 )}{( s ) ^{2} ( s + 100 ) ^{2} ( s + 400 )}

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- \frac{1}{( e ^{t} + e ^{- t} ) ^{2}}