MATH SOLVE

4 months ago

Q:
# Simplify the expression square root of -1 over (3+8i)-(2+5i)

Accepted Solution

A:

Comment

I'm taking this to mean

[tex]\frac{ \sqrt{-1} }{(3 + 8i) - (2 + 5i)} [/tex]

Step One

Simplify the denominator

3 + 8i - 2 - 5i

1 + 3i

Step Two

rewrite the numerator in terms of i.

sqrt(-1) = i

Step 3

rewrite the fraction

[tex] \frac{i}{1 + 3i} [/tex]

Step 4

Rationalize the denominator. Multiply top and bottom by (1 - 3i)

[tex] \frac{i * (1 - 3i)}{(1 - 3i)(1 + 3i)} [/tex]

Step 5

Simplify the denominator.

[tex] \frac{i*(1 - 3i)}{(1 - 9i^2)} [/tex]

[tex] \frac{i* (1 - 3i)}{1 + 9} = \frac{i*(1 - 3i)}{10} [/tex]

Step Six

Remove the brackets in the numerator.

[tex] \frac{i + 4}{10}\text{ I'll leave you to figure out the numerator} [/tex]

I'm taking this to mean

[tex]\frac{ \sqrt{-1} }{(3 + 8i) - (2 + 5i)} [/tex]

Step One

Simplify the denominator

3 + 8i - 2 - 5i

1 + 3i

Step Two

rewrite the numerator in terms of i.

sqrt(-1) = i

Step 3

rewrite the fraction

[tex] \frac{i}{1 + 3i} [/tex]

Step 4

Rationalize the denominator. Multiply top and bottom by (1 - 3i)

[tex] \frac{i * (1 - 3i)}{(1 - 3i)(1 + 3i)} [/tex]

Step 5

Simplify the denominator.

[tex] \frac{i*(1 - 3i)}{(1 - 9i^2)} [/tex]

[tex] \frac{i* (1 - 3i)}{1 + 9} = \frac{i*(1 - 3i)}{10} [/tex]

Step Six

Remove the brackets in the numerator.

[tex] \frac{i + 4}{10}\text{ I'll leave you to figure out the numerator} [/tex]