math and algebra
4
I assume that "I" is a variable2+5i+6+3i7i+6+3i10i+616i is the answer
To simplify the expression ((7 - 3i)(-11 + 5i)), use the distributive property (FOIL method). First, multiply the real parts: (7 \cdot -11 = -77). Next, multiply the outer parts: (7 \cdot 5i = 35i), then the inner parts: (-3i \cdot -11 = 33i), and finally the last parts: (-3i \cdot 5i = -15i^2). Combine the results: (-77 + 35i + 33i + 15) (since (i^2 = -1)) simplifies to (-62 + 68i). Thus, the simplified expression is (-62 + 68i).
0.4
i is the Imaginary Unit, equal to sqrt(-1). So i and any real number multiplied by i will all be imaginary numbers. Here are some: i, -i, 5i, -3i, i*pi, etc.
The conjugate of 2 + 3i is 2 - 3i, and the conjugate of 2 - 5i is 2 + 5i.
Complex ; 9 - 5i It conjugate is ' 9 + 5i'.
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.
4
negative 15 is the answer
I assume that "I" is a variable2+5i+6+3i7i+6+3i10i+616i is the answer
2
-4-3i
0.4
Use the Pythagorean theorem. 5, -5, 5i, and -5i will work, as well as any combination of a real and imaginary number such that (real part) squared + (imaginary part) squared = 25, for example, 4 + 3i, 3 + 4i, 4 - 3i, etc.
1/(2 + 5i) (multiply both the numerator and the denominator by 2 - 5i)= 1(2 - 5i)/(2 + 5i)(2 - 5i)= (2 - 5i)/(4 - 25i2) (substitute -1 for i2)= (2 - 5i)/(4 + 25)= (2 - 5i)/29= 2/29 - (5/29)i
1/(3+5i)=(3-5i)/((3+5i)(3-5i))=(3-5i)/(9+25)=(3-5i)/34