simplify (3+mi)^2

Solution

simplify

(3 + mi)^{2}

(9 - m^{2}) + 6 mi

Solution steps

(3 + mi)^{2}

Apply Perfect Square Formula:

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

(3 + mi)^{2} = 3^{2} + 2 \cdot 3 mi + (mi)^{2}

= 3^{2} + 2 \cdot 3 mi + (mi)^{2}

3^{2} = 9

2 \cdot 3 mi = 6 mi

(mi)^{2} = - m^{2}

= 9 + 6 mi - m^{2}

Rewrite in standard complex form:

(9 - m^{2}) + 6 mi

= (9 - m^{2}) + 6 mi

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