Complex Numbers quiz #1 Flashcards
Complex Numbers quiz #1
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In which quadrant of the complex plane is the complex number 6 – 8i located? The complex number 6 – 8i has a positive real part (6) and a negative imaginary part (–8). On the complex plane, this places it in the fourth quadrant. What is the standard form of a complex number and what do the variables represent? The standard form is a + bi, where a is the real part and b is the imaginary part. The variable b is the coefficient of the imaginary unit i. How do you identify the real and imaginary parts in the complex number 0 + 7i? The real part is 0 and the imaginary part is 7. The number can be written as 7i, but as a complex number, the real part is still 0. When adding complex numbers, what should you do with the imaginary unit 'i'? Treat 'i' as if it were a variable and combine like terms. Add the real parts together and the imaginary parts together. What is the result of multiplying two complex numbers that are conjugates of each other? Multiplying a complex number by its conjugate always results in a real number. The result is a^2 + b^2 if the original number is a + bi. What is the purpose of multiplying the numerator and denominator by the conjugate when dividing complex numbers? Multiplying by the conjugate eliminates the imaginary unit from the denominator. This allows the denominator to become a real number. How do you simplify an expression involving i squared when multiplying complex numbers? Replace i squared with -1 in the expression. This allows you to combine and simplify the terms further. What happens to the middle terms when you multiply a complex number by its conjugate? The middle terms cancel each other out. This leaves only real terms in the result. After dividing complex numbers and simplifying, how should you express your final answer? Express the answer in standard form as a + bi, separating the real and imaginary parts. Each part should have the denominator included if it is a fraction. What is the complex conjugate of the number -1 + 2i? The complex conjugate is -1 - 2i. Only the sign of the imaginary part changes.
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