Digital ACT Math Practice Question #871
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To eliminate \( i \) from the denominator, multiply both numerator and denominator by the complex conjugate of \( 3 - 4i \), which is \( 3 + 4i \).
Remember that \( i^2 = -1 \). In the numerator, \( 8i^2 \) becomes \( 8(-1) = -8 \), which subtracts from 15 to give 7.
To simplify a complex quotient, multiply the numerator and denominator by the complex conjugate of the denominator \( (3 + 4i) \): \[ \frac{(5 + 2i)(3 + 4i)}{(3 - 4i)(3 + 4i)} \] Denominator: \( 3^2 - (4i)^2 = 9 - 16(-1) = 9 + 16 = 25 \). N...
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