Simplify Radicals and Imaginary Numbers Review

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

How do you simplify √12?

Back

√12 can be simplified to 2√3.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as √-1.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

What is the pattern for powers of i?

Back

The powers of i cycle every four: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1.

Front

How do you multiply two complex numbers?

Back

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

Front

What is the result of (4 – 3i)(-7 – 2i)?

Back

The result is -34 + 13i.

Front

How do you subtract complex numbers?

Back

To subtract (a + bi) - (c + di), subtract the real parts and the imaginary parts separately.

Front

What is the result of (10 + 15i) - (48 - 30i)?

Back

The result is -38 + 45i.

Front

How do you simplify -√-8?

Back

-√-8 simplifies to -2i√2.