Multiplication of two complex numbers is also a complex number. In other words, the product of two complex numbers can be expressed in the standard form A + iB where A and B are real.

The utility of the conjugate is that any complex number multiplied by its complex conjugate is a real number: This operation has practical utility for the rationalization of complex numbers and the square root of the number times its conjugate is the magnitude of the complex number when expressed in polar form.

The conjugate of the product of the two complex numbers is equal to the product of the conjugates of the numbers.

The product of two conjugate complex numbers is a real number. Multiplying two conjugates is equivalent to finding the product of the sum and difference of two numbers.

The product of complex conjugates is a difference of two squares it is always a real number. The product a complex conjugates may be written in standard form as a + bi where neither a nor b is zero. The product of complex conjugates is a sum of two squares and is always a real number.

If the imaginary part is positive then the conjugate will contain imaginary part negative and if the imaginary part is negative then the conjugate will contain imaginary part positive. Here 5i is the imaginary part and is positive therefore the conjugate of 5i is −5i .

Conjugate math definition Conjugates in math are two pairs of binomials with identical terms but sharing opposite operations in the middle. Below are a few more examples of pairs of conjugates: x – y and x + y. 2√2 – 1 and 2√2 + 1.

The conjugate of a complex number a + bi (with real coefficients a, b) is what you get when you “replace” i with -i, namely a – bi. For example, the conjugate of i is -i, the “other” square root of -1.

The complex conjugate of a complex number is a complex number that can be obtained by changing the sign of the imaginary part of the given complex number. For example, the complex conjugate of 2 + 3i is 2 – 3i.

Therefore, the complex conjugate of 3−7i is 3+7i .

3+7i is a complex number. It is NOT a pure imaginary.

A conjugate is the same two term expression but with the sign in the middle changed. So, for example, if you have 3+√2, the conjugate would be 3−√2.