Divide and simplify to the form a+bi.
(-8+i)/(2-3i)
To divide and simplify the expression (-8+i)/(2-3i) to the form a+bi, we can follow these steps:
Step 1: Multiply the numerator and denominator by the conjugate of the denominator, which is (2+3i). This will help us get rid of the complex denominator.
(-8+i)(2+3i)
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(2-3i)(2+3i)
Step 2: Apply the distributive property and perform the multiplication in the numerator and denominator.
Numerator: (-8)(2) + (-8)(3i) + (i)(2) + (i)(3i) = -16 -24i + 2i + 3i^2 = -16 -22i + 3i^2
Denominator: (2)(2) + (2)(3i) - (3i)(2) - (3i)(3i) = 4 + 6i - 6i - 9i^2 = 4 - 9i^2
Step 3: Simplify the terms involving i.
Numerator: -16 -22i + 3i^2 = -16 -22i + 3(-1) = -16 -22i - 3 = -19 - 22i
Denominator: 4 - 9i^2 = 4 - 9(-1) = 4 + 9 = 13
Step 4: Divide the numerator by the denominator.
(-19 - 22i) / 13
Therefore, the expression (-8+i)/(2-3i) simplifies to (-19 - 22i) / 13 in the form a+bi.