Enough said.
-
Think of a rule you learned when studying quadratic equations: (a + b) * (a - b) = a^2 - b^2
If we used the term, a + b and a - b are conjugates.
Imagine instead a + bi. The conjugate is a - bi, so that
(a + bi)(a - bi) = a^2 + b^2
If we used the term, a + b and a - b are conjugates.
Imagine instead a + bi. The conjugate is a - bi, so that
(a + bi)(a - bi) = a^2 + b^2
-
Let the complex number = Z and the conjugate = Z َ
z = a + bi
z َ = a - bi
Only on the imaginary part (bi)
Examples :
3+5i \\\ 3-5i
i \\\ - i
7 \\\\ 7 ( there isn't imaginary part in here 7+0i = 7 - 0i )
the conjugate important rules
Z * Z َ = a^2 + b ^ 2
Z + Z َ = 2a
z = a + bi
z َ = a - bi
Only on the imaginary part (bi)
Examples :
3+5i \\\ 3-5i
i \\\ - i
7 \\\\ 7 ( there isn't imaginary part in here 7+0i = 7 - 0i )
the conjugate important rules
Z * Z َ = a^2 + b ^ 2
Z + Z َ = 2a
-
given a complex number z =a +bi , its conjugate is z* = a - bi
-
the complex conjugate of a+bi is a-bi