If it's not what You are looking for type in the equation solver your own equation and let us solve it.
Simplifying (2 + 5i)(3 + -7i) = -1 + -1i Multiply (2 + 5i) * (3 + -7i) (2(3 + -7i) + 5i * (3 + -7i)) = -1 + -1i ((3 * 2 + -7i * 2) + 5i * (3 + -7i)) = -1 + -1i ((6 + -14i) + 5i * (3 + -7i)) = -1 + -1i (6 + -14i + (3 * 5i + -7i * 5i)) = -1 + -1i (6 + -14i + (15i + -35i2)) = -1 + -1i Combine like terms: -14i + 15i = 1i (6 + 1i + -35i2) = -1 + -1i Solving 6 + 1i + -35i2 = -1 + -1i Solving for variable 'i'. Reorder the terms: 6 + 1 + 1i + i + -35i2 = -1 + -1i + 1 + i Combine like terms: 6 + 1 = 7 7 + 1i + i + -35i2 = -1 + -1i + 1 + i Combine like terms: 1i + i = 2i 7 + 2i + -35i2 = -1 + -1i + 1 + i Reorder the terms: 7 + 2i + -35i2 = -1 + 1 + -1i + i Combine like terms: -1 + 1 = 0 7 + 2i + -35i2 = 0 + -1i + i 7 + 2i + -35i2 = -1i + i Combine like terms: -1i + i = 0 7 + 2i + -35i2 = 0 Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -0.2 + -0.05714285714i + i2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.05714285714i + 0.2 + i2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.05714285714i + i2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.05714285714i + i2 = 0 + 0.2 -0.05714285714i + i2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.05714285714i + i2 = 0.2 The i term is -0.05714285714i. Take half its coefficient (-0.02857142857). Square it (0.0008163265305) and add it to both sides. Add '0.0008163265305' to each side of the equation. -0.05714285714i + 0.0008163265305 + i2 = 0.2 + 0.0008163265305 Reorder the terms: 0.0008163265305 + -0.05714285714i + i2 = 0.2 + 0.0008163265305 Combine like terms: 0.2 + 0.0008163265305 = 0.2008163265305 0.0008163265305 + -0.05714285714i + i2 = 0.2008163265305 Factor a perfect square on the left side: (i + -0.02857142857)(i + -0.02857142857) = 0.2008163265305 Calculate the square root of the right side: 0.448125347 Break this problem into two subproblems by setting (i + -0.02857142857) equal to 0.448125347 and -0.448125347.Subproblem 1
i + -0.02857142857 = 0.448125347 Simplifying i + -0.02857142857 = 0.448125347 Reorder the terms: -0.02857142857 + i = 0.448125347 Solving -0.02857142857 + i = 0.448125347 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '0.02857142857' to each side of the equation. -0.02857142857 + 0.02857142857 + i = 0.448125347 + 0.02857142857 Combine like terms: -0.02857142857 + 0.02857142857 = 0.00000000000 0.00000000000 + i = 0.448125347 + 0.02857142857 i = 0.448125347 + 0.02857142857 Combine like terms: 0.448125347 + 0.02857142857 = 0.47669677557 i = 0.47669677557 Simplifying i = 0.47669677557Subproblem 2
i + -0.02857142857 = -0.448125347 Simplifying i + -0.02857142857 = -0.448125347 Reorder the terms: -0.02857142857 + i = -0.448125347 Solving -0.02857142857 + i = -0.448125347 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '0.02857142857' to each side of the equation. -0.02857142857 + 0.02857142857 + i = -0.448125347 + 0.02857142857 Combine like terms: -0.02857142857 + 0.02857142857 = 0.00000000000 0.00000000000 + i = -0.448125347 + 0.02857142857 i = -0.448125347 + 0.02857142857 Combine like terms: -0.448125347 + 0.02857142857 = -0.41955391843 i = -0.41955391843 Simplifying i = -0.41955391843Solution
The solution to the problem is based on the solutions from the subproblems. i = {0.47669677557, -0.41955391843}
| 5=11x^2-176 | | 29=-35x+14 | | x-3=7x+35 | | 3(x+6)-8=5x+2(x-3) | | f(x)=-x-1 | | 4+11x=84 | | 5x-12=-3x+36 | | x-5=i | | x=i | | x-5+x*6=34 | | 10/0.02 | | 3x+31=x+13 | | Log[3](5x-7)=1 | | 4(2x+3)-(5x+2)=73 | | A=1/3A+160000 | | a^2+2ab+b^2=x | | 7x^2+32x-45=0 | | x^2-2x-68= | | x^2-y^2=289 | | 2x+4x=2 | | a+a+b+a+b+a+b= | | 4x+3y+9z-2x+5z-5y= | | 10x-2000+x^2= | | 5x-1=9x-2 | | 7x+b=41 | | 5-2x=2x-3 | | 5(b+2)=35 | | 3(p+5)=21 | | 9(y-2)=9 | | 5(3X+6)+2(x+2)=49 | | 6(x+3)=29(X-1) | | 4(a+7)=44 |