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What purpose does the complex conjugate serve in complex number arithmetic?
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The complex conjugate is used to rationalize denominators in fractions involving complex numbers.
How are complex numbers plotted on a plane?
The real part is plotted on the x-axis (Real Number Axis) and the imaginary part is plotted on the y-axis (Imaginary Axis).
Identify the real and imaginary parts of the complex number (-2/7) + (-4/7)i.
Real part: -2/7, Imaginary part: -4/7.
How do you represent the imaginary unit 'i' in terms of radicals?
The imaginary unit 'i' is represented as the square root of -1, i.e., i = √(-1).
Solve the quadratic equation x² + 8x + 17 = 0 using the quadratic formula.
The solutions are x = 4 ± i.
What is the definition of a complex number?
A complex number has a real part 'a' and an imaginary part 'b' associated with 'i' (√(-1)), represented as 'a + bi'.
Explain why √a * √b ≠ √(ab) when both 'a' and 'b' are negative.
For negative numbers under separate radicals, the product of their square roots is not the square root of their product.
Compute and identify the real and imaginary parts of: ( -1 + i ) - ( 6 - 9i ).
The result is -7 + 10i. Real part: -7, Imaginary part: 10.
What happens to the sign of the imaginary part when finding the complex conjugate of a number?
The sign of the imaginary part is reversed.
What is the value of i²?
i² = -1.
Rationalize the denominator of (3 - 4i) / (1 - 3i).
Multiply by the complex conjugate: (3 - 4i)(1 + 3i) / (1 - 3i)(1 + 3i). Simplify: (15 + 5i) / 10 = (3/2) + (1/2)i.
What is the complex conjugate of (7 + 2i)?
The complex conjugate is (7 - 2i).
Add the complex numbers ( -5 + 5i ) and ( 7 - i ). What are the real and imaginary parts of the result?
The result is 2 + 4i. Real part: 2, Imaginary part: 4.
What is obtained when multiplying (6 + i) and (1 - 4i)?
The result is 10 + 2i. Real part: 10, Imaginary part: 2.
Given the complex number 3 + 8i, identify the real and imaginary parts.
Real part: 3, Imaginary part: 8
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