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Complete the following equation. Your answers will be algebraic expressions. (a+bi)^2= _____ + 2abiHint: think of i as an ordinary variable and then replace i^2 with -1.

Sagot :

The given expression is:

[tex](a+ib)^2[/tex]

Expand to get:

[tex]\begin{gathered} (a+ib)^2=a^2+i^2b^2+2abi \\ =a^2-b^2+2abi \end{gathered}[/tex]

The value is as above since it is given that i^2=-1.

So the expansion is:

[tex](a+ib)^2=a^2-b^2+2abi[/tex]

The blank should be:

[tex]a^2-b^2[/tex]

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