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Popular >

simplify (z+2i)^2

Solution

simplify

(z + 2 i)^{2}

Solution

(z^{2} - 4) + 4 z 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 z \cdot 2 i + (2 i)^{2}

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

2 z \cdot 2 i = 4 z i

(2 i)^{2} = - 4

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

Rewrite in standard complex form:

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

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

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Frequently Asked Questions (FAQ)

What is (z+2i)^2 ?
The solution to (z+2i)^2 is (z^2-4)+4zi