(a +bi)(c + di) : Use the distributive property and remember i*i = -1. In polar form:|ab| = |ab| and thetaab = thetaa + thetab.
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If y = a + bi and z = c + di are two complex numbers then z - y = (c - a) + (d - b)i
The four possible combinations are:A = (+, +)B = (+, -)C = (-, +) andD = (-, -)In A and D, the two numbers have the same signs and the multiplication gives a positive answer.In B and C, the two numbers have different signs and the multiplication gives a negative answer.
Yes. Multiplication of any real numbers has the associative property: (a x b) x c = a x (b x c)
Numbers of the form a + ib (where i = -11/2; a and b are real numbers) are called complex numbers.For any two complex numbers (a+ib) and (c+id):Addition:(a+ib) + (c+id) = (a+c) + i(b+d)So, -8i-7i = (-8-7)i = -15i
Real numbers are a proper subset of complex numbers. In fact each complex number, z, can be represented as z = x +iy where x and y are real numbers and i is the imaginary square root of -1.Thus the set of complex numbers is the Cartesian product of two sets of real numbers. That is, C = R x R where C is the set of complex numbers and R is the set of real numbers. Limitations of this browser prevent me from writing that in a mathematically precise and more helpful fashion.