document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #271634 by CharlesG2(834)![]() ![]() ![]() 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?\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "see if this helps at all: \n" ); document.write( "a real number is any number that you usually work with such as: \n" ); document.write( "integers (..., -3, -2, -1, 0, 1, 2, 3,...), \n" ); document.write( "or rational numbers (numbers that can be expressed as a fraction, \n" ); document.write( "such as 3/4 or 1/2 or 1/3), \n" ); document.write( "or irrational numbers (such as pi, e, sqrt(2), sqrt(3)) \n" ); document.write( "a complex number is different from a real number, \n" ); document.write( "it is of form a + bi where a and b are real numbers, \n" ); document.write( "you may also see this expressed as x + yi where x and y are real numbers \n" ); document.write( "also the imaginary number i is the square root of -1 and i^2 = -1 \n" ); document.write( "addition: \n" ); document.write( "(a + bi) + (c + di) = a + c + (b + d)i \n" ); document.write( "subtraction: \n" ); document.write( "(a + bi) - (c + di) = a - c + (b - d)i \n" ); document.write( "multiplication (here you will have to use FOIL or First Outer Inner Last): \n" ); document.write( "(a + bi)(c + di) = ac + adi + bci + bdi^2 = ac - bd + (ad + bc)i \n" ); document.write( "division (here you will have to multiply numerator and denominator \n" ); document.write( "by the conjugate (a + bi conjugate is a - bi) of the denominator): \n" ); document.write( "(a + bi)/(c + di) = ((a + bi)(c - di))/((c + di)(c - di)) \n" ); document.write( "(a + bi)/(c + di) = (ac - adi + bci - bdi^2)/(c^2 - d^2*i^2) \n" ); document.write( "(a + bi)/(c + di) = (ac + bd + (bc - ad)i)/(c^2 + d^2) \n" ); document.write( "(a + bi)/(c + di) = (ac + bd)/(c^2 + d^2) + ((bc - ad)/(c^2 + d^2))i\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |