1.2 Complex numbers (in class)

Evaluate the following numbers.

(a) [math]3i-2i^3[/math]

(b) [math]3-i+(4+2i)[/math]

(c) [math]\dfrac{2}{i}+\dfrac{i}{2}[/math]

(d) [math](3-i)(4+5i)[/math]

If [math]\sqrt{-2}\cdot(-\sqrt{-12})=a\sqrt{b}[/math] where [math]a[/math] and [math]b[/math] are real numbers, what is the value of [math]a[/math] and [math]b[/math]?

If [math]\dfrac{\sqrt{6}}{\sqrt{-2}-\sqrt{-8}}=\sqrt{a}i[/math] where [math]a[/math]is a real number, what is the value of [math]a[/math]?

If [math](\sqrt{-3}+\sqrt{5})^2=a+2\sqrt{b}i[/math] where [math]a[/math] and [math]b[/math] are real numbers, what are the values of [math]a[/math] and [math]b[/math]?

If [math]A=x+(y+5)i[/math] and [math]B=9-y+xi[/math] where [math]x, y\in\mathbb{R}[/math] and [math]A=B[/math], what is the value of [math]x+y[/math]?

Let [math]C=2+a-2ai+7i[/math] where [math]a[/math] is a constant.

(a) If [math]a\in\mathbb{R}[/math] and [math]C[/math] is a pure imaginary number, what is the value of [math]a[/math]?

(b) If [math]a[/math] is a pure imaginary number and [math]C[/math] is a real number, what is the value of [math]-ai[/math]?

If [math](-2-\sqrt{-32})-(4+\sqrt{-18})=a+b\sqrt{2}i[/math] where [math]a[/math] and [math]b[/math] are constants, what is the value of [math]a+b[/math]?

If [math](6-\sqrt{-7})(-4+\sqrt{-7})=a+b\sqrt{c}[/math] where [math]a, b[/math], and [math]c[/math] are integers, what is the value of [math]a+b+c[/math]?