simplify (7+4i)^2

Solution

simplify

(7 + 4 i)^{2}

33 + 56 i

Solution steps

(7 + 4 i)^{2}

Apply Perfect Square Formula:

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

(7 + 4 i)^{2} = 7^{2} + 2 \cdot 7 \cdot 4 i + (4 i)^{2}

= 7^{2} + 2 \cdot 7 \cdot 4 i + (4 i)^{2}

Simplify

7^{2} + 2 \cdot 7 \cdot 4 i + (4 i)^{2} : 56 i + 33

= 56 i + 33

Rewrite in standard complex form:

33 + 56 i

= 33 + 56 i

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