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Popular >

simplify (3z+5i)^2

Solution

simplify

(3 z + 5 i)^{2}

Solution

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

Solution steps

(3 z + 5 i)^{2}

Apply Perfect Square Formula:

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

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

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

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

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

(5 i)^{2} = - 25

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

Rewrite in standard complex form:

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

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

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Frequently Asked Questions (FAQ)

What is (3z+5i)^2 ?
The solution to (3z+5i)^2 is (9z^2-25)+30zi