Last Flashcard: Imaginary & Complex

Front

What is the value of i^7?

Back

-i

Front

Simplify the division problem: (2-4i)/(1+3i)

Back

-1-i

Front

Which expression is equivalent to (-6 + i)²?

Back

35 - 12i

Front

What is the complex conjugate of 4-3i?

Back

4 + 3i

Front

Simplify \sqrt{-18}.

Back

3i\sqrt{2}

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

The imaginary unit i is defined as the square root of -1, i.e., i = \sqrt{-1}.

Front

What is the formula for the modulus of a complex number z = a + bi?

Back

The modulus of z is given by |z| = \sqrt{a^2 + b^2}.

Front

How do you find the argument of a complex number?

Back

The argument of a complex number z = a + bi is given by \theta = \tan^{-1}(\frac{b}{a}).

Front

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

Back

The result is a^2 + b^2.