simplify (1-3zi)^2

Solution

simplify

(1 - 3 z i)^{2}

(1 - 9 z^{2}) - 6 z i

Solution steps

(1 - 3 z i)^{2}

Apply Perfect Square Formula:

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

(1 - 3 z i)^{2} = 1^{2} - 2 \cdot 1 \cdot 3 z i + (3 z i)^{2}

= 1^{2} - 2 \cdot 1 \cdot 3 z i + (3 z i)^{2}

1^{2} = 1

- 2 \cdot 1 \cdot 3 z i = - 6 z i

(3 z i)^{2} = - 9 z^{2}

= 1 - 6 z i - 9 z^{2}

Rewrite in standard complex form:

(1 - 9 z^{2}) - 6 z i

= (1 - 9 z^{2}) - 6 z i

(cos (2 x) - sin (2 x))^{2}

cos (\frac{7 π}{3})

lo g_{10} (7) (3 x - 2)^{2}

\frac{n ( n + 1 )}{2}

(9 x^{2} - 6 x + 81) arccsc (9 x^{2})