Complex Number | Common Mistake (1)

Multiplication of complex numbers remains the same as done for normal algebraic operation.

However, due to complex number having 2 terms, namely, real and imaginary terms, care has to be taken for the "i"unit.

This is specially so when multiplication of conjugate is involved.

A popular mistake made while doing this form of multiplication is:

(3 + i2)(3 - i2) = 3² + (i2)²

What is wrong?

The concept of conjugate and its multiplication states that:
(a + ib)(a - ib) = a² + b²

The "i" symbol is NOT reflection in the final outcome!

Only the "a" and the "b", the numerical part, are extracted out for computation.

Taking the "i" into account will cause the sign of the last term (i2) to be incorrect.
This is because i² = -1.

Therefore, regardless of the sign in the multiplicands, just pull out the numerical part in the complex number and use them for calculation, that is, the 3 and 2 in the example above.

The correct answer, thus, is (3 + i2)(3 - i2) = 3² + 2².

Looking carefully at the application of the formula, you will notice that this is a simple and easy technique to do conjugate multiplication.

Message: "Touch me not" i said.

Mastery takes place when we do not repeat mistakes.

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