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Popular >

simplify (3z+4i)^2

Solution

simplify

(3 z + 4 i)^{2}

Solution

(9 z^{2} - 16) + 24 z i

Solution steps

(3 z + 4 i)^{2}

Apply Perfect Square Formula:

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

(3 z + 4 i)^{2} = (3 z)^{2} + 2 \cdot 3 z \cdot 4 i + (4 i)^{2}

= (3 z)^{2} + 2 \cdot 3 z \cdot 4 i + (4 i)^{2}

(3 z)^{2} = 9 z^{2}

2 \cdot 3 z \cdot 4 i = 24 z i

(4 i)^{2} = - 16

= 9 z^{2} + 24 z i - 16

Rewrite in standard complex form:

(9 z^{2} - 16) + 24 z i

= (9 z^{2} - 16) + 24 z i

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Frequently Asked Questions (FAQ)

What is (3z+4i)^2 ?
The solution to (3z+4i)^2 is (9z^2-16)+24zi