Identify the complex number and its conjugate.

Welcome back Jacinta — missed you this week. To express the complex number in Cartesian form, we multiply the numerator and the denominator by the conjugate of the denominator. Step 1: Identify the complex number and its conjugate. The given complex number is (2+5i)/(-2-3i). The denominator is -2-3i. Its conjugate is -2+3i. Step 2: Multiply the numerator and denominator by the conjugate. (2+5i)/(-2-3i) × (-2+3i)/(-2+3i) Step 3: Expand the numerator and the denominator. Numerator: (2+5i)(-2+3i) = 2(-2) + 2(3i) + 5i(-2) + 5i(3i) = -4 + 6i - 10i + 15i^2 Since i^2 = -1: = -4 - 4i + 15(-1) = -4 - 4i - 15 = -19 - 4i Denominator: (-2-3i)(-2+3i) = (-2)^2 - (3i)^2 = 4 - 9i^2 Since i^2 = -1: = 4 - 9(-1) = 4 + 9 = 13 Step 4: Combine the simplified numerator and denominator. (-19 - 4i)/(13) Step 5: Express in Cartesian form a+bi. -(19)/(13) - (4)/(13)i The Cartesian form is -(19)/(13) - (4)/(13)i. Send me the next one 📸