Question

Divide (-3-3i) by (3-4i) and write your answer as a complex number in standard form?

Answer 1

To divide complex numbers, we use the conjugate of the denominator. Multiply the numerator and denominator by the conjugate, simplify, and write the answer in standard form.

Step-by-step explanation:

To divide complex numbers, we use the conjugate of the denominator. The conjugate of 3-4i is 3+4i. We multiply the numerator and denominator by the conjugate, simplify, and write the answer in standard form.

Step 1: Multiply the numerator and denominator by the conjugate of the denominator:
(-3-3i)(3+4i)/(3-4i)(3+4i)

Step 2: Simplify:
(-3)(3)+(-3)(4i)+(-3i)(3)+(-3i)(4i)/(3)(3)+(3)(4i)+(-4i)(3)+(-4i)(4i)

Step 3: Simplify further:
-9-12i-9i+12i^2/9+12i-12i-16i^2

Step 4: Simplify the imaginary terms:
-9-21i+12(-1)/9-16(-1)

Step 5: Simplify further:
{-9+12(-1)} / {9-16(-1)}

Step 6: Evaluate:
{-9-12} / {9+16}

Step 7: Simplify the complex number:
-21/25

Learn more about dividing complex numbers