Answer: (-4+7i)/13.
- A (4+7i)/13
- B (4-7i)/13
- C (-4-7i)/13
- D (-4+7i)/13
Correct answer: D. (-4+7i)/13
Explanation: Multiply by conjugate: (1+2i)(2+3i)/((2-3i)(2+3i)) = (2+3i+4i+6i<sup>2</sup>)/(4+9) = (2+7i-6)/13 = (-4+7i)/13. Numerator: (2-6)+(3+4)i = -4+7i. So (-4+7i)/13.
A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.
Concept context
Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots
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