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4. If z, a+bi and z, c+di represent two complex numbers with real components a, b, c and d, then which of the following represents the coefficient of i in the product of z, and z,?

(1) ac-bd

(2) ad-be

(3) ab+cd

(4) be+ad

2 Answers

3 votes

Final answer:

The coefficient of 'i' in the product of the two complex numbers 'a+bi' and 'c+di' is (ad + bc).

Step-by-step explanation:

To determine the coefficient of i in the product of two complex numbers z, a+bi and z, c+di, we perform the multiplication:

(a + bi)(c + di) = ac + adi + bci + bidi

Combining like terms, we get:

ac + (ad + bc)i + bdi2

Since i2 = -1, this simplifies to:

ac - bd + (ad + bc)i

Therefore, the coefficient of i in the product is (ad + bc).

User CiucaS
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2 votes

Answer:3

Step-by-step explanation:

User Qba
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