Imaginary and Complex Numbers

Front

What is the square root of a negative number represented as?

Back

The square root of a negative number is represented using the imaginary unit 'i', where √-a = i√a.

Front

How do you simplify √-108?

Back

√-108 = √(108) * √(-1) = 6i√3.

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is written as a + bi, where 'a' is the real part and 'bi' is the imaginary part.

Front

What is the imaginary part of the complex number a + bi?

Back

The imaginary part is 'bi'.

Front

How do you multiply two complex numbers (4 + 3i)(4 - 3i)?

Back

(4 + 3i)(4 - 3i) = 4^2 - (3i)^2 = 16 - (-9) = 25.

Front

What is the result of adding two complex numbers (5 - 2i) + (-7 + 8i)?

Back

The result is (-2 + 6i).

Front

What is the value of i^2?

Back

i^2 = -1.

Front

How do you express a complex number in polar form?

Back

A complex number can be expressed in polar form as r(cos θ + i sin θ), where r is the modulus and θ is the argument.

Front

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

Back

The modulus is given by |a + bi| = √(a^2 + b^2).

Front

What is the argument of a complex number?

Back

The argument of a complex number is the angle θ formed with the positive real axis, often calculated using tan(θ) = b/a.