Example Question - division problem solution
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Mathematical Division Problem Solution
The image shows a mathematical division problem where the dividend is 6 and the divisor is 3. To solve for the quotient: \[ 6 \div 3 = ? \] The division of 6 by 3 equals 2. So the answer to the division problem is: \[ 6 \div 3 = 2 \]
Solving Division of Complex Numbers
The division problem shown in the image is asking you to divide a complex number, -5, by another complex number, -3 - i. To solve this, you can write the division as a fraction and then multiply the numerator and denominator by the conjugate of the denominator. The conjugate of a complex number changes the sign of the imaginary part, so the conjugate of -3 - i is -3 + i. Here's how you do it step by step: \[\frac{-5}{-3 - i} \times \frac{-3 + i}{-3 + i} = \frac{-5(-3 + i)}{(-3 - i)(-3 + i)}\] Now multiply the numerators and the denominators: \[= \frac{15 - 5i}{(-3)^2 - (i)^2}\] Since \(i^2 = -1\), the denominator becomes: \[(-3)^2 - (-1) = 9 + 1 = 10\] Thus the expression simplifies to: \[= \frac{15 - 5i}{10}\] Now divide both real and imaginary parts by 10: \[= \frac{15}{10} - \frac{5i}{10}\] Reducing these fractions we have: \[= \frac{3}{2} - \frac{1}{2}i\] So the answer to the division problem is: \[1.5 - 0.5i\] or in fraction form \[\frac{3}{2} - \frac{1}{2}i\].
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