simplify (z^2+i)^2

Solution

simplify

(z^{2} + i)^{2}

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

Solution steps

(z^{2} + i)^{2}

Apply Perfect Square Formula:

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

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

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

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

i^{2} = - 1

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

Rewrite in standard complex form:

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

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

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