simplify (1+5zi)^2

Solution

simplify

(1 + 5 z i)^{2}

(1 - 25 z^{2}) + 10 z i

Solution steps

(1 + 5 z i)^{2}

Apply Perfect Square Formula:

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

(1 + 5 z i)^{2} = 1^{2} + 2 \cdot 1 \cdot 5 z i + (5 z i)^{2}

= 1^{2} + 2 \cdot 1 \cdot 5 z i + (5 z i)^{2}

1^{2} = 1

2 \cdot 1 \cdot 5 z i = 10 z i

(5 z i)^{2} = - 25 z^{2}

= 1 + 10 z i - 25 z^{2}

Rewrite in standard complex form:

(1 - 25 z^{2}) + 10 z i

= (1 - 25 z^{2}) + 10 z i

(x + sin (y) - cos (y)) d x + x (sin (y) + cos (y)) d y

(x - y)^{2}

(f + g) (π)

(x + 1 + 1)^{2}

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