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Popular >

simplify (z-i)^2

Solution

simplify

(z - i)^{2}

Solution

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

Solution steps

(z - i)^{2}

Apply Perfect Square Formula:

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

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

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

Apply imaginary number rule:

i^{2} = - 1

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

Rewrite in standard complex form:

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

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

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Frequently Asked Questions (FAQ)

What is (z-i)^2 ?
The solution to (z-i)^2 is (z^2-1)-2zi