Question

Which equation illustrates the identity property of multiplication?
(a + bi) × c = (ac + bci)
(a + bi) × 0 = 0
(a + bi) × (c + di) = (c + di) × (a + bi)
(a + bi) × 1 = (a + bi)

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which equation illustrates the identity property of multiplication

• (a + bi) × c = (ac + bci)

• (a + bi) × 0 = 0

• (a + bi) × (c + di) = (c + di) × (a + bi)

• (a + bi) × 1 = (a + bi)

CONCEPT TO BE IMPLEMENTED

Complex Number

A complex number z = a + ib is defined as an ordered pair of Real numbers ( a, b) that satisfies the following conditions :

(i) Condition for equality :

(a, b) = (c, d) if and only if a = c, b = d

(ii) Definition of addition :

(a, b) + (c, d) = (a+c, b+ d)

(iii) Definition of multiplication :

(a, b). (c, d) = (ac-bd , ad+bc )

Of the ordered pair (a, b) the first component a is called Real part of z and the second component b is called Imaginary part of z

EVALUATION

Let (a + bi) be an complex number

Now 1 is the Multiplicative identity

So that (a + bi) × 1 = (a + bi) = 1 × (a+bi)

FINAL ANSWER

The correct option is

(a + bi) × 1 = (a + bi)

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