4i(-2 -3i) = 4i×-2 - 4i×-3i = -8i -12i² = -8i + 12 = 12 -8i
→ the conjugate is 12 + 8i
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The conjugate is 7 - 3i is 7 + 3i.
The complex conjugate of a number in the form a + bi is simply the same number with the sign of the imaginary part changed. In this case, the number is 7 + 3i, so its complex conjugate would be 7 - 3i. This is because the complex conjugate reflects the number across the real axis on the complex plane.
0+3i has a complex conjugate of 0-3i thus when you multiply them together (0+3i)(0-3i)= 0-9i2 i2= -1 0--9 = 0+9 =9 conjugates are used to eliminate the imaginary parts
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When adding and subtracting complex numbers, you can treat the "i" as any variable. For example, 5i + 3i = 8i, 5i -3i = 2i, etc.; (2 + 5i) - (3 - 3i) = (2 - 3) + (5 + 3)i = -1 + 8i.