Q: Why the conjugation only change the sign of the imaginary part?

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The conjugate of a complex number can be found by multiplying the imaginary part by -1, then adding the "real" part back. (-2i) * -1 = 2i, so the conjugation is 7+2i

Let a and b be real numbers, then (a + bi)(a - bi) (complex conjugates) = a2 - b2i2 by definition i2 = -1 = a2 + b2 (the sum of two real numbers is also a real number)

No. A complex number is a number that has both a real part and an imaginary part. Technically, a pure imaginary number ... which has no real part ... is not a complex number.

The imaginary part is expressed as a product of i(square root of negative one), typically following a plus sign, so that the complex number has the form a + bi, with "a" the real part and "bi" the imaginary part.

A complex number has a real part and a (purely) imaginary part, So imaginary numbers are a subset of complex numbers. But the converse is not true. A real number is also a member of the complex domain but it is not an imaginary number.

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The conjugate of a complex number can be found by multiplying the imaginary part by -1, then adding the "real" part back. (-2i) * -1 = 2i, so the conjugation is 7+2i

Let a and b be real numbers, then (a + bi)(a - bi) (complex conjugates) = a2 - b2i2 by definition i2 = -1 = a2 + b2 (the sum of two real numbers is also a real number)

No. A complex number consists of a real part and a imaginary part. If the real part equals zero, there is only the imaginary left and you could therefor argue that it is an imaginary number (or else it would still be a complex number -with a real part=0)

You convert the real part and the imaginary parts separately.

The second principal part of a verb in the third conjugation will end in -Δre.

All the verbs that end in -o in the first principal part and -ere in the second principal part. Note: some people count verbs that end in -io in the first principal part and -ere in the second principal part as third conjugation. However, others place it in a different conjugation called 'third -io conjugation.'

Verb

No. A complex number is a number that has both a real part and an imaginary part. Technically, a pure imaginary number ... which has no real part ... is not a complex number.

No. All Complex Numbers are of the form a + bi where a and b are Real Numbers and i is the square root of -1. So only ones where a = 0 are pure Imaginary Numbers.

The word "imaginary" can function as both an adjective and a noun. As an adjective, it describes something that exists only in the imagination. As a noun, "imaginary" refers to the mental process of creating images or ideas that do not actually exist.

Real part of the result = real part of first number + real part of second number Imaginary part of the result = imaginary part of first number + imaginary part of second number

The word "imaginary" is an adjective.