Divide and simplify to the form a+bi.
(-8+i)/(2-3i)
You have to remember that i² = -1.
so, when you apply the distributive property:
(-8+i)/(2-3i) = -8*2 + 8*3*i + 2*i - 3i²
= -16 + 26*i +3
Is the answer (23/13)+(43/13)i
To divide and simplify the expression (-8+i)/(2-3i) to the form a+bi, you can follow these steps:
Step 1: Multiply both the numerator and denominator by the conjugate of the denominator.
The conjugate of 2-3i is 2+3i. Multiply both the numerator and denominator by 2+3i:
((-8+i)/(2-3i)) * ((2+3i)/(2+3i))
Step 2: Simplify the expression by multiplying the numerators and denominators.
((-8+i) * (2+3i))/((2-3i) * (2+3i))
Step 3: Apply the FOIL method to multiply the numerators and denominators.
((-8 * 2) + (-8 * 3i) + (i * 2) + (i * 3i))/((2 * 2) + (2 * 3i) + (-3i * 2) + (-3i * 3i))
Simplifying further:
(-16 - 24i + 2i + 3i^2)/(4 + 6i - 6i - 9i^2)
Since i^2 is defined as -1:
(-16 - 24i + 2i + 3(-1))/(4 + 0 - 0 - 9(-1))
Simplifying further:
(-16 - 24i + 2i - 3)/(4 + 9)
(-19 - 22i)/(13)
So the final simplified expression would be -19/13 - (22/13)i.