Question 383580: I need help with complex numbers. We have been working on them all week, but it's a little hard to understand. Will you help me?
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! I need help with complex numbers. We have been working on them all week, but it's a little hard to understand. Will you help me?
see if this helps at all:
a real number is any number that you usually work with such as:
integers (..., -3, -2, -1, 0, 1, 2, 3,...),
or rational numbers (numbers that can be expressed as a fraction,
such as 3/4 or 1/2 or 1/3),
or irrational numbers (such as pi, e, sqrt(2), sqrt(3))
a complex number is different from a real number,
it is of form a + bi where a and b are real numbers,
you may also see this expressed as x + yi where x and y are real numbers
also the imaginary number i is the square root of -1 and i^2 = -1
addition:
(a + bi) + (c + di) = a + c + (b + d)i
subtraction:
(a + bi) - (c + di) = a - c + (b - d)i
multiplication (here you will have to use FOIL or First Outer Inner Last):
(a + bi)(c + di) = ac + adi + bci + bdi^2 = ac - bd + (ad + bc)i
division (here you will have to multiply numerator and denominator
by the conjugate (a + bi conjugate is a - bi) of the denominator):
(a + bi)/(c + di) = ((a + bi)(c - di))/((c + di)(c - di))
(a + bi)/(c + di) = (ac - adi + bci - bdi^2)/(c^2 - d^2*i^2)
(a + bi)/(c + di) = (ac + bd + (bc - ad)i)/(c^2 + d^2)
(a + bi)/(c + di) = (ac + bd)/(c^2 + d^2) + ((bc - ad)/(c^2 + d^2))i
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