BackMultiplying and Dividing Complex Numbers quiz
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1/15BackSkip to main contentBackWhat is the standard form for expressing a complex number after multiplication?
The standard form is a + bi, where a is the real part and b is the imaginary part. What is the value of i squared (i^2) and how is it used when multiplying complex numbers?
i^2 equals -1; it is used to simplify terms involving i^2 during multiplication. When multiplying (3i) by (7 - 2i), what is the result in standard form?
The result is 6 + 21i. What method is used to multiply two complex numbers, each with two terms?
The FOIL method is used to multiply two binomial complex numbers. What is the result of multiplying (-6 + 2i) by (3 + 4i) in standard form?
The result is -26 - 18i. How do you find the complex conjugate of a complex number a + bi?
Reverse the sign of the imaginary part; the conjugate is a - bi. What is the complex conjugate of 1 + 2i?
The complex conjugate is 1 - 2i. What happens when you multiply a complex number by its conjugate?
The result is always a real number. What shortcut can you use when multiplying a complex number by its conjugate?
The product is a^2 + b^2, where a and b are the real and imaginary parts. Why do we multiply by the complex conjugate when dividing complex numbers?
Multiplying by the conjugate eliminates i from the denominator, making it real. What is the result of dividing 3 by (1 + 2i) and expressing it in standard form?
The result is (3/5) - (6/5)i. What are the four possible values for powers of i?
The four values are i, -1, -i, and 1. What is the value of i to the 4th power (i^4)?
i^4 equals 1. How do you quickly determine the value of i raised to a high power, like i^100?
Divide the exponent by 4; if the remainder is 0, the value is 1. If the remainder after dividing the exponent by 4 is 2, what is the value of i to that power?
The value is -1, since i^2 equals -1.
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