Solve Z=(2-5i)(2+5i)

$$Z = ( 2 - 5 i ) ( 2 + 5 i )$$

Solve for Z

$$Z=29$$

Steps for Solving Linear Equation

Multiply complex numbers 2-5i and 2+5i like you multiply binomials.

$$Z=2\times 2+2\times \left(5i\right)-5i\times 2-5\times 5i^{2}$$

By definition, i^{2} is -1.

$$Z=2\times 2+2\times \left(5i\right)-5i\times 2-5\times 5\left(-1\right)$$

Do the multiplications in 2\times 2+2\times \left(5i\right)-5i\times 2-5\times 5\left(-1\right).

$$Z=4+10i-10i+25$$

Combine the real and imaginary parts in 4+10i-10i+25.

$$Z=4+25+\left(10-10\right)i$$

Do the additions in 4+25+\left(10-10\right)i.

$$Z=29$$

Assign Z

$$Z≔29$$