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  We hope that work with the complex number is quite easy because you can work with imaginary unit i as a variable. And use definition i 2 = -1 to simplify complex expressions. Many operations are the same as operations with two-dimensional vectors. Addition Very simple, add up the real parts (without i) and add up the imaginary parts (with i): This is equal to use rule: (a+b i )+(c+d i ) = (a+c) + (b+d) i (1+i) + (6-5i) = 7-4i 12 + 6-5i = 18-5i (10-5i) + (-5+5i) = 5 Subtraction Again very simple, subtract the real parts and subtract the imaginary parts (with i): This is equal to use rule: (a+b i )+(c+d i ) = (a-c) + (b-d) i (1+i) - (3-5i) = -2+6i -1/2 - (6-5i) = -6.5+5i (10-5i) - (-5+5i) = 15-10i Multiplication To multiply two complex numbers, use distributive law, avoid binomials, and apply i 2 = -1 . This is equal to use rule: (a+b i )(c+d i ) = (ac-bd) + (ad+bc) i (1+i) (3+5i) = 1*3+1*5i+i*3+i*5i = 3+5i+3i-5 = -2+8i -1/2 * (6-5i) = -3+2.5i (10-5i) * (-5+5i) = -25+75i Division

  The essential price method entails figuring out "likely" or "unlikely" with the aid of using figuring out whether or not or now no longer the found check statistic is extra intense than could be anticipated if the null speculation had been true. That is, it involves evaluating the found check statistic to a few cutoff prices, known as the " essential price ." If the check statistic is extra intense than the essential price, then the null speculation is rejected in want of the opportunity speculation.  If the check statistic isn't always as intense because of the essential price, then the null speculation isn't always rejected. Specifically, the 4 steps concerned in the usage of the essential price method to undertaking any speculation check are: Specify the null and opportunity hypotheses . Using the pattern information and assuming the null speculation is true, calculate the price of the check statistic. To behavior the speculation check for the