You must be logged in to see worked solutions.

Already have an account? Log in here.

De Moivre's Theorem shows that to raise a complex number to the nth power, the absolute value is raised to the nth power and the argument is multiplied by n.

Let \(z\) be a complex number such that \[z = \sqrt{2}(\cos 7 ^{\circ} + i \sin 7 ^{\circ}).\] Then \( z^{8} \) can be expressed as \( r( \cos \alpha^{\circ} + i \sin \alpha^{\circ}) \), where \(r\) is a real number and \( 0 \leq \alpha \leq 90\). What is the value of \(r+\alpha ?\)

**Details and assumptions**

\(i\) is the imaginary unit, where \(i^2=-1\).

You must be logged in to see worked solutions.

Already have an account? Log in here.

The two roots of \( f(x) = x^2 + 20x + 200 \) can be written in the form \( a \pm bi \). What is \( b-a, \) assuming \(b > 0 \)?

**Details and assumptions**

\( i \) is defined as the imaginary unit, such that \( i^2 = -1 \).

You must be logged in to see worked solutions.

Already have an account? Log in here.

You must be logged in to see worked solutions.

Already have an account? Log in here.

Let \(a+bi\) and \(c+di\) be the two roots of the quadratic equation \[x^2+25=0,\] where \(b>d\). What is the value of \(ac-bd\)?

**Details and assumptions**

\(i\) is the imaginary number that satisfies \(i^2 = -1\).

You must be logged in to see worked solutions.

Already have an account? Log in here.

You must be logged in to see worked solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...