Imaginary & Complex Numbers

Front

What is the value of i^7?

Back

-i

Front

Rationalize the denominator and simplify: \( \frac{-3-i}{4} \)

Back

\( \frac{-3-i}{4} \)

Front

Rationalize the denominator and simplify: \( \frac{7-13i}{26} \)

Back

\( \frac{7-13i}{26} \)

Front

Simplify \( \sqrt{-81} \)

Back

9i

Front

What is the value of i^13?

Back

i

Front

Define imaginary numbers.

Back

Imaginary numbers are numbers that can be written as a real number multiplied by the imaginary unit i, where i is defined as \( i = \sqrt{-1} \).

Front

What is the definition of complex numbers?

Back

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form \( a + bi \), where a and b are real numbers.

Front

What is the conjugate of a complex number \( a + bi \)?

Back

The conjugate of a complex number \( a + bi \) is \( a - bi \).

Front

How do you multiply two complex numbers \( (a + bi)(c + di) \)?

Back

Use the distributive property: \( ac + adi + bci + bdi^2 \) and simplify using \( i^2 = -1 \).

Front

What is the modulus of a complex number \( a + bi \)?

Back

The modulus is given by \( |a + bi| = \sqrt{a^2 + b^2} \).