Algebra 2 Radicals and Complex Numbers

Algebra 2 Radicals and Complex Numbers
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Simplify the expression. Show your work.
Solution:

4x23y is the same as 4*√x23y= 2x3ySimplify the expression. Show your work.
Solution:

Opening the brackets;
3*1+3*5i-4i*1 -4i*5i-2-iCollecting like terms;
3+15i-4i-20i2-2-i3+11i-20i2-2+i
1+12i-20i2The formula represents the length of the hypotenuse of a right triangle with side lengths a and b. Solve the equation for b. Show your work.
Solution:

Finding the square of both sides gives:
c2= a2+b2b2= c2- a2Now find the square roots in both sides. Therefore,
b =c2-a2