simplify (5z+3i)^2

Solution

simplify

(5 z + 3 i)^{2}

(25 z^{2} - 9) + 30 z i

Solution steps

(5 z + 3 i)^{2}

Apply Perfect Square Formula:

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

(5 z + 3 i)^{2} = (5 z)^{2} + 2 \cdot 5 z \cdot 3 i + (3 i)^{2}

= (5 z)^{2} + 2 \cdot 5 z \cdot 3 i + (3 i)^{2}

(5 z)^{2} = 25 z^{2}

2 \cdot 5 z \cdot 3 i = 30 z i

(3 i)^{2} = - 9

= 25 z^{2} + 30 z i - 9

Rewrite in standard complex form:

(25 z^{2} - 9) + 30 z i

= (25 z^{2} - 9) + 30 z i

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