How do you perform the operation and write the result in standard form given #(12i)^2(1+2i)^2#?
Expand each bracket using, say ,the FOIL method.
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To perform the operation and write the result in standard form, follow these steps:

Expand each binomial expression: [ (1  2i)^2 = (1  2i)(1  2i) ] [ (1 + 2i)^2 = (1 + 2i)(1 + 2i) ]

Use the distributive property to multiply each pair of binomials.

Combine like terms and simplify.
Let's start with expanding each binomial expression:
[ (1  2i)^2 = (1  2i)(1  2i) ] [ = 1(1) + 1(2i)  2i(1)  2i(2i) ] [ = 1  2i  2i + 4i^2 ] [ = 1  4i  4(1) ] [ = 1  4i + 4 ] [ = 5  4i ]
[ (1 + 2i)^2 = (1 + 2i)(1 + 2i) ] [ = 1(1) + 1(2i) + 2i(1) + 2i(2i) ] [ = 1 + 2i + 2i + 4i^2 ] [ = 1 + 4i + 4(1) ] [ = 1 + 4i  4 ] [ = 3 + 4i ]
Now, subtract the second expression from the first:
[ (1  2i)^2  (1 + 2i)^2 = (5  4i)  (3 + 4i) ] [ = 5  4i + 3  4i ] [ = 8  8i ]
So, the result in standard form is ( 8  8i ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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