Complex Numbers pre-before and after

Front

What is the value of i^72?

Back

1

Front

What is the standard form of a complex number?

Back

A complex number is in standard form if it is expressed as a + bi, where a and b are real numbers and i is the imaginary unit.

Front

How do you simplify i^n for any integer n?

Back

To simplify i^n, divide n by 4 and use the remainder to determine the value: 0 -> 1, 1 -> i, 2 -> -1, 3 -> -i.

Front

What is the result of (5 + 3i)(5 - 3i)?

Back

34, because it is a difference of squares: (5^2 - (3i)^2) = 25 - (-9) = 34.

Front

What is i^3?

Back

i^3 = -i.

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers.

Front

What is the imaginary unit i?

Back

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

Front

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

Back

The conjugate is a - bi.

Front

How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately.

Front

How do you multiply two complex numbers?

Back

To multiply (a + bi)(c + di), use the distributive property: ac + adi + bci + bdi^2, and simplify.