Multiply Complex Numbers

What is the imaginary unit 'i'?

• The imaginary unit 'i' is defined as the square root of -1.

• The imaginary unit 'i' is defined as the square root of 0.

• The imaginary unit 'i' is defined as the square root of 1.

• The imaginary unit 'i' is defined as the square root of 2.

What is a complex number?

• A number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

• A number that is always positive and can be represented on a number line.

• A number that can only be expressed as a fraction of two integers.

• A number that has no real part and is purely imaginary.

How do you add two complex numbers?

• To add two complex numbers, multiply their real parts and their imaginary parts separately: (a + bi) * (c + di) = (ac - bd) + (ad + bc)i.

• To add two complex numbers, simply add their real parts and their imaginary parts separately: (a + bi) + (c + di) = (a + c) + (b + d)i.

• To add two complex numbers, subtract their imaginary parts and add their real parts: (a + bi) - (c + di) = (a - c) + (b + d)i.

• To add two complex numbers, take the average of their real parts and the average of their imaginary parts: (a + bi) + (c + di) = ((a + c)/2) + ((b + d)/2)i.

What is the product of a complex number and its conjugate?

• a^2 + b^2

• a^2 - b^2

• 2ab

• a^2 + 2b

How can complex numbers be used in real-world applications?

• In signal processing, control theory, and fluid dynamics.

• Only in theoretical mathematics.

• To solve simple arithmetic problems.

• In basic geometry and algebra.

How do you express a complex number in polar form?

• r(cos θ + i sin θ)

• r + iθ

• r(θ + i)

• cos θ + sin θ

How do you divide two complex numbers?

• Multiply the numerator and denominator by the conjugate of the denominator, then simplify.

• Add the real parts and the imaginary parts separately.

• Subtract the imaginary part from the real part of the numerator.

• Multiply the denominator by its reciprocal.

What is the conjugate of a complex number a + bi?

• a + bi

• a - bi

• -a + bi

• -a - bi

What is the geometric interpretation of complex numbers?

• Complex numbers can be represented as points or vectors in a two-dimensional plane, known as the complex plane, where the x-axis represents the real part and the y-axis represents the imaginary part.

• Complex numbers are represented as single-dimensional values on a number line.

• Complex numbers can only be represented as real numbers in a three-dimensional space.

• Complex numbers have no geometric interpretation and are purely algebraic.

What is the modulus of a complex number a + bi?

• |a + bi| = √(a^2 + b^2)

• |a + bi| = a^2 + b^2

• |a + bi| = a + b

• |a + bi| = √(a + b)