Solve 3t+12it=4)

$$3 t + 12 i t = 4 )$$

Solve for t

$$t=\frac{4}{51}-\frac{16}{51}i\approx 0.078431373-0.31372549i$$

Steps for Solving Linear Equation

Combine 3t and 12it to get \left(3+12i\right)t.

$$\left(3+12i\right)t=4$$

Divide both sides by 3+12i.

$$t=\frac{4}{3+12i}$$

Multiply both numerator and denominator of \frac{4}{3+12i} by the complex conjugate of the denominator, 3-12i.

$$t=\frac{4\left(3-12i\right)}{\left(3+12i\right)\left(3-12i\right)}$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$t=\frac{4\left(3-12i\right)}{3^{2}-12^{2}i^{2}}$$

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

$$t=\frac{4\left(3-12i\right)}{153}$$

Multiply 4 times 3-12i.

$$t=\frac{4\times 3+4\times \left(-12i\right)}{153}$$

Do the multiplications in 4\times 3+4\times \left(-12i\right).

$$t=\frac{12-48i}{153}$$

Divide 12-48i by 153 to get \frac{4}{51}-\frac{16}{51}i.

$$t=\frac{4}{51}-\frac{16}{51}i$$