(2i-1)(2i+1) = ????????????????

(2i - 1)(2i + 1)
= 2i(2i) + 2i(1) - 1(2i) - 1(1)
= 4i^2 + 2i - 2i - 1
= 4(-1) - 1
= -4 - 1
= -5

(2i-1)(2i+1)

Arrange the expression into the a+bi form of a complex number.

(-1+2i)(1+2i)

Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.

-1*1-1*2i+2i*1+2i*2i

Multiply -1 by 1 to get -1.

-1-1*2i+2i*1+2i*2i

Multiply -1 by 2i to get -2i.

-1-2i+2i*1+2i*2i

Multiply 2i by 1 to get 2i.

-1-2i+2i+2i*2i

Multiply 2i by 2i to get 4i^2

-1-2i+2i+4i^2

According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, i is a factor of both -2i and 2i.

-1+(-2+2)i+4i^2

To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value. In this example, subtract the absolute values of -2 and 2 and give the result the same sign as the integer with the greater absolute value.

-1+(0)i+4i^2

Remove the parentheses.

-1+4i^2

i raised to the 2 power is -1.

-1+4*-1

Multiply 4 by -1 to get -4.

-1-4

Subtract 4 from -1 to get -5.

-5

Formula
( a - b ) ( a + b ) = a^2 - b^2
Here
2i = a and 1 = b
( 2i - 1 ) ( 2i + 1) = ( 2i ) ^2 - ( 1 )^2
( 2i - 1 ) ( 2i + 1) = 4i^2 - 1

(2i-1)(2i+1) = 2i x 2i + 2i x 1 + (-1) x 2i + (-1) x 1 = 4i^2 + 2i - 2i - 1 = 4i^2 - 1

4 i ² - 1
- 4 - 1
- 5