Operations with Radicals and Complex Numbers

Front

What is the value of i^2?

Back

-1

Front

Define 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

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

Front

Simplify: √(16)

Back

4

Front

Simplify: √(x^2)

Back

|x| (the absolute value of x)

Front

What is the product of two complex conjugates (a + bi)(a - bi)?

Back

a^2 + b^2.

Front

Simplify: (3 + 4i) + (2 - 3i)

Back

5 + i

Front

Simplify: (1 + 2i)(3 - 4i)

Back

11 - i

Front

What is the conjugate of the complex number 5 + 6i?

Back

5 - 6i.

Front

What is the modulus of the complex number 3 + 4i?

Back

5 (calculated as √(3^2 + 4^2)).