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Questions and Answers
Given $z = 3 - 2i$ and $w = 3 + 4i$, what is the product, $zw$?
Given $z = 3 - 2i$ and $w = 3 + 4i$, what is the product, $zw$?
- $1 - 6i$
- $17 - 6i$
- $17 + 6i$ (correct)
- $1 + 6i$
If $z = a + bi$ is a complex number, what is the complex conjugate of $z$?
If $z = a + bi$ is a complex number, what is the complex conjugate of $z$?
- $a - bi$ (correct)
- $-a + bi$
- $b + ai$
- $-a - bi$
What is the value of $i^2$, where $i$ is the imaginary unit?
What is the value of $i^2$, where $i$ is the imaginary unit?
- 1
- -1 (correct)
- 0
- 2
Which of the following represents a complex number?
Which of the following represents a complex number?
What is the real part of the complex number $7 - 5i$?
What is the real part of the complex number $7 - 5i$?
Flashcards
What is a complex number?
What is a complex number?
Complex numbers are expressed in the form a + bi, where 'a' is the real part and 'b' is the imaginary part, and 'i' is the imaginary unit (√-1).
What is the value of i²?
What is the value of i²?
The imaginary unit 'i' is defined as the square root of -1 (i = √-1). Therefore, i² = -1.
How to multiply complex numbers?
How to multiply complex numbers?
To multiply complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi². Remember that i² = -1.
Multiply: (3 - 2i)(3 + 4i)
Multiply: (3 - 2i)(3 + 4i)
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What is (3 - 2i) * (3 + 4i)?
What is (3 - 2i) * (3 + 4i)?
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Study Notes
- Given z = 3 - 2i and w = 3 + 4i, the task is to find the result of zw (z multiplied by w).
- This is question 7, asking to select the correct answer from the options provided.
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Description
Multiply two complex numbers z and w. Find the real and imaginary parts of the product zw. This involves applying the distributive property and simplifying using i^2 = -1.
