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Popular >

simplify (a+bi)^2

Solution

simplify

(a + bi)^{2}

Solution

(a^{2} - b^{2}) + 2 abi

Solution steps

(a + bi)^{2}

Apply Perfect Square Formula:

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

(a + bi)^{2} = a^{2} + 2 abi + (bi)^{2}

= a^{2} + 2 abi + (bi)^{2}

Simplify

(bi)^{2} : - b^{2}

= a^{2} + 2 abi - b^{2}

Rewrite in standard complex form:

(a^{2} - b^{2}) + 2 abi

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

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Frequently Asked Questions (FAQ)

What is (a+bi)^2 ?
The solution to (a+bi)^2 is (a^2-b^2)+2abi