simplify (9+5i)^2

Solution

simplify

(9 + 5 i)^{2}

56 + 90 i

Solution steps

(9 + 5 i)^{2}

Apply Perfect Square Formula:

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

(9 + 5 i)^{2} = 9^{2} + 2 \cdot 9 \cdot 5 i + (5 i)^{2}

= 9^{2} + 2 \cdot 9 \cdot 5 i + (5 i)^{2}

Simplify

9^{2} + 2 \cdot 9 \cdot 5 i + (5 i)^{2} : 90 i + 56

= 90 i + 56

Rewrite in standard complex form:

56 + 90 i

= 56 + 90 i

1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{x}}}}

16900

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