The complex conjugate of a+bi is a-bi.
This is written as z* where z is a complex number.
ex.
z = a+bi
z* = a-bi
r = 3+12i
r* = 3-12i
s = 5-6i
s* = 5+6i
t = -3+7i = 7i-3
t* = -3-7i = -(3+7i)
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The product is a^2 + b^2.
Complex numbers form: a + bi where a and b are real numbers. The conjugate of a + bi is a - bi If you multiply a complex number by its conjugate, the product will be a real number, such as (a + bi)(a - bi) = a2 - (bi)2 = a2 - b2i2 = a2 - b2(-1) = a2 + b2
For a complex number (a + bi), its conjugate is (a - bi). If the number is graphically plotted on the Complex Plane as [a,b], where the Real number is the horizontal component and Imaginary is vertical component, the Complex Conjugate is the point which is reflected across the real (horizontal) axis.
8 - 8i
This might be a complex number and its conjugate: (a + bi) times (a - bi). More generally, any two complex numbers such that the angle formed by one is the negative of the angle formed by the other. In other words, you can multiply the conjugate by any real constant and still get a real result: (a + bi) times (ca - cbi). Specific examples: Multiply (3 + 2i) times (3 - 2i). Multiply (3 + 2i) times (6 - 4i).