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Dividing multiplies numerator and denominator by the conjugate of the denominator, which makes the denominator the real number c² + d². The moduli divide and the arguments subtract.
Complex division
(a + bi)/(c + di) = [(ac + bd) + (bc − ad)i] / (c² + d²)
The denominator's modulus squared is 25, giving (15 − 40)/25 + (30 + 20)/25·i = −1 + 2i.
Because (c + di)(c − di) = c² + d² is real, which clears the imaginary part from the denominator.