simplify (4-yi)^2

Solution

simplify

(4 - y i)^{2}

(16 - y^{2}) - 8 y i

Solution steps

(4 - y i)^{2}

Apply Perfect Square Formula:

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

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

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

4^{2} = 16

- 2 \cdot 4 y i = - 8 y i

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

= 16 - 8 y i - y^{2}

Rewrite in standard complex form:

(16 - y^{2}) - 8 y i

= (16 - y^{2}) - 8 y i

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