Question

If x = a + bi and y = c + di, x × y = y × x.

Answer 1

In mathematics, complex numbers can be multiplied using the formula (ac - bd) + (ad + bc)i. The multiplication of complex numbers is commutative, meaning that x × y is equal to y × x.

Step-by-step explanation:

In mathematics, when we multiply two complex numbers, x = a + bi and y = c + di, the result is given by the formula:

x × y = (a + bi) × (c + di) = (ac - bd) + (ad + bc)i

The multiplication of complex numbers is commutative, which means that x × y is equal to y × x. Therefore, the statement x × y = y × x is true.

Answer 2

x = a + bi
y = c + di

xy = yx
(a + bi)(c + di) = (c + di)(a + bi)
a(c + di) + bi(c + di) = c(a + bi) + di(a + bi)
a(c) + a(di) + bi(c) + bi(di) = c(a) + c(bi) + di(a) + di(bi)
ac + adi + bci + bdi² = ac + bci + adi + bdi²
ac + adi + bci - bd = ac + bci + adi - bd