(a+bi)*(a-bi)=

Solution for (a+bi)*(a-bi)= equation:

Simplifying
(a + bi)(a + -1bi) = 0

Multiply (a + bi) * (a + -1bi)
(a(a + -1bi) + bi(a + -1bi)) = 0
((a * a + -1bi * a) + bi(a + -1bi)) = 0

Reorder the terms:
((-1abi + a2) + bi(a + -1bi)) = 0
((-1abi + a2) + bi(a + -1bi)) = 0
(-1abi + a2 + (a * bi + -1bi * bi)) = 0
(-1abi + a2 + (abi + -1b2i2)) = 0

Reorder the terms:
(-1abi + abi + a2 + -1b2i2) = 0

Combine like terms: -1abi + abi = 0
(0 + a2 + -1b2i2) = 0
(a2 + -1b2i2) = 0

Solving
a2 + -1b2i2 = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add 'b2i2' to each side of the equation.
a2 + -1b2i2 + b2i2 = 0 + b2i2

Combine like terms: -1b2i2 + b2i2 = 0
a2 + 0 = 0 + b2i2
a2 = 0 + b2i2
Remove the zero:
a2 = b2i2

Simplifying
a2 = b2i2

Take the square root of each side:
a = {-1bi, bi}