In problems like this, you are expected to simplify by removing i from the denominator. To do this, multiply the numerator and denominator by the conjugate of the denominator (switch the sign between the two terms from either a plus to a minus or vice versa) over itself. The conjugate over itself equals 1 and does not change the value of the expression (any number multiplied by 1 is still that number). Multiplying by the conjugate is the only way to eliminate i since there will be no middle term when we foil.

Simplify i squared to be -1 and combine like terms

Since every term divides by 8 make sure to reduce all the terms by that greatest common factor

In problems like this, you are expected to simplify by removing i from the denominator. To do this, multiply the numerator and denominator by the conjugate of the denominator (switch the sign between the two terms from either a plus to a minus or vice versa) over itself. The conjugate over itself equals 1 and does not change the value of the expression (any number multiplied by 1 is still that number). Multiplying by the conjugate is the only way to eliminate i since there will be no middle term when we foil.

Simplify i squared to be -1 and then combine like terms

To see what the polar form of the number is, it helps to draw it on a graph, where the horizontal axis is the imaginary part and the vertical axis the real part. This is called the complex plane.

To find the angle , we can find its supplementary angle  and subtract it from  radians, so .

Using trigonometric ratios,    and  .

Then .

To find the distance , we need to find the distance from the origin to the point . Using the Pythagorean Theorem to find the hypotenuse ,  or .

Step 1: Re-write the log equation as an exponential equation. To do this, take the base of the log function and raise it to the number on the right side of the equal sign. This new exponent is equal to the number to the right of the log base.



Step 2: Re-write the right hand side as a power of 4..



Step 3: Re-write the equation



Step 4: We have the same base, so we can equal the exponents..

In order to solve for x, we must first rewrite the log in exponential form. 

Every log is written in the below general form: 

In this case we have: 

This becomes: 

We can solve this by taking the square root of both sides: 

Use rules of logarithms...

Take the base of the log and raise it to the number on the right side of the equal sign (which becomes the exponent):

Step 1: Write the expression in exponential form...

Given: 

Step 2: Convert the right hand side into a power of 6..

Step 3: Re-write the equations...

Since the bases are equal, taking log of both sides will cancel them.

Recall a few properties of logarithms:

1.When adding logarithms of like base, we multiply the inside.

2.When subtracting logarithms of like base, we divide the inside.

3. When multiplying a logarithm by a number, we can raise the inside to that power.

So we begin with this:

I would start with 3 to simplify the first log.

Next, use rule 1 on the first two logs.

Then, use rule 2 to combine these two.

So our answer is 6.06.

When combining logarithms into one log, we must remember that addition and multiplication are linked and subtraction and division are linked. 

In this case we have multiplication and division - so we assume anything that is negative, must be placed in the bottom of the fraction.