Flashcard on Operations with Radicals and Complex Numbers

Front

What is the value of i^52?

Back

1

Front

Simplify the expression: \( \frac{2-7i}{4i} \)

Back

\( \frac{-7-2i}{4} \)

Front

What is the value of i^97?

Back

i

Front

Add/Subtract: (7 + 2i) - (-12 - 4i)

Back

19 + 6i

Front

Simplify: \( \sqrt{150} \)

Back

5\sqrt{6}

Front

What is the definition of 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 and i is the imaginary unit.

Front

What is the imaginary unit i?

Back

i is defined as the square root of -1, i.e., \( i = \sqrt{-1} \).

Front

What is the principal square root of a negative number?

Back

The principal square root of a negative number is expressed in terms of i, e.g., \( \sqrt{-a} = i\sqrt{a} \).

Front

How do you add complex numbers?

Back

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

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract their real parts and their imaginary parts separately.