Chapter 1: Complex Numbers - Summary of Key Points-Questions and Answers Graded A+
Chapter 1: Complex Numbers - Summary of Key Points-Questions and Answers Graded A+ i = - ANSWER-√-1 i² = - ANSWER--1 imaginary number - ANSWER-bi complex number - ANSWER-a + bi if b² - 4ac 0 - ANSWER-then ax²+bx+c has two complex solutions which are a conjugate pair if z = a + bi - ANSWER-its complex conjugate z* = a - bi if roots are α and β - ANSWER-equation can be written as: (z-α)(z-β) = 0 or z² - (α+β)z +αβ = 0 for cubic equation with real coefficients - ANSWER-- all 3 roots are real - one root is real and the other two are a complex conjugate pair for quartic equation with real coefficients - ANSWER-- all 4 roots are real - two are real and two are a complex conjugate pair - two pairs of complex conjugates Complex number - ANSWER-Real + imaginary parts Imaginary number - ANSWER-When squared, gives a negative number. Therefore, "j = √-1" Imaginary number polar - ANSWER-Can be represented with polar co-ordinates. "j" is a unit vector with a 90° phase shift. Polar - complex - ANSWER-Z = Z(cos β + j sin β) Three phase system characteristics - ANSWER-∑V = 0 Phases separated by 120°
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