simplify (1+yi)^2

Solution

simplify

(1 + y i)^{2}

(1 - y^{2}) + 2 y i

Solution steps

(1 + y i)^{2}

Apply Perfect Square Formula:

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

(1 + y i)^{2} = 1^{2} + 2 \cdot 1 \cdot y i + (y i)^{2}

= 1^{2} + 2 \cdot 1 \cdot y i + (y i)^{2}

1^{2} = 1

2 \cdot 1 \cdot y i = 2 y i

(y i)^{2} = - y^{2}

= 1 + 2 y i - y^{2}

Rewrite in standard complex form:

(1 - y^{2}) + 2 y i

= (1 - y^{2}) + 2 y i

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