simplify (z^4-i)^2

Solution

simplify

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

(z^{8} - 1) - 2 z^{4} i

Solution steps

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

Apply Perfect Square Formula:

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

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

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

(z^{4})^{2} = z^{8}

i^{2} = - 1

= z^{8} - 2 z^{4} i - 1

Rewrite in standard complex form:

(z^{8} - 1) - 2 z^{4} i

= (z^{8} - 1) - 2 z^{4} i

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