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z* is the complex conjugate of z therefore z* = x - yi. So 16 + 32i = 5(x + yi)-3(x - yi), real: 16 = 5x - 3x => 16=2x => x=8, imaginary: 32 = 5y + 3y => 32 = 8y => y=4, therefore z = 8 + 4i.<...

Use the formula (n-2)*180 where n is the number of sides on the polygon.

If two lines are parallel, then they will have the same gradient. The gradient of the curve is represented by m in the equation y=mx + c. For this question, if L2 is parallel to L1, m will therefore equal...

4(3x-2)=2x-5
Expand the brackets: 4(3x)-4(2)=2x-5 ---> 12x-8=2x-5Collect like terms, but beware of sign changes: 12x-2x-8=-5 (subtract 2 from both sides of the equation) -----> 10x...

To solve this problem we will use the principle of conservation of energy. The gravitational potential energy of the ball at the maximum height must be equal to the kinetics energy at the bottom plus the ...