Solve (4i+3i^2)(1-i)/(1-i)(1-i)

$$\frac { ( 4 i + 3 i ^ { 2 } ) ( 1 - i ) } { ( 1 - i ) ( 1 - i ) }$$

Evaluate

$$-\frac{7}{2}+\frac{1}{2}i=-3.5+0.5i$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{3i^{2}+4i}{\left(1-i\right)\left(1-i\right)^{0}}$$

Calculate i to the power of 2 and get -1.

$$\frac{3\left(-1\right)+4i}{\left(1-i\right)\left(1-i\right)^{0}}$$

Multiply 3 and -1 to get -3.

$$\frac{-3+4i}{\left(1-i\right)\left(1-i\right)^{0}}$$

To multiply powers of the same base, add their exponents. Add 1 and 0 to get 1.

$$\frac{-3+4i}{\left(1-i\right)^{1}}$$

Calculate 1-i to the power of 1 and get 1-i.

$$\frac{-3+4i}{1-i}$$

Multiply both numerator and denominator by the complex conjugate of the denominator, 1+i.

$$\frac{\left(-3+4i\right)\left(1+i\right)}{\left(1-i\right)\left(1+i\right)}$$

Do the multiplications in \frac{\left(-3+4i\right)\left(1+i\right)}{\left(1-i\right)\left(1+i\right)}.

$$\frac{-7+i}{2}$$

Divide -7+i by 2 to get -\frac{7}{2}+\frac{1}{2}i.

$$-\frac{7}{2}+\frac{1}{2}i$$

Real Part

$$-\frac{7}{2} = -3\frac{1}{2} = -3.5$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$Re(\frac{3i^{2}+4i}{\left(1-i\right)\left(1-i\right)^{0}})$$

Calculate i to the power of 2 and get -1.

$$Re(\frac{3\left(-1\right)+4i}{\left(1-i\right)\left(1-i\right)^{0}})$$

Multiply 3 and -1 to get -3.

$$Re(\frac{-3+4i}{\left(1-i\right)\left(1-i\right)^{0}})$$

To multiply powers of the same base, add their exponents. Add 1 and 0 to get 1.

$$Re(\frac{-3+4i}{\left(1-i\right)^{1}})$$

Calculate 1-i to the power of 1 and get 1-i.

$$Re(\frac{-3+4i}{1-i})$$

Multiply both numerator and denominator of \frac{-3+4i}{1-i} by the complex conjugate of the denominator, 1+i.

$$Re(\frac{\left(-3+4i\right)\left(1+i\right)}{\left(1-i\right)\left(1+i\right)})$$

Do the multiplications in \frac{\left(-3+4i\right)\left(1+i\right)}{\left(1-i\right)\left(1+i\right)}.

$$Re(\frac{-7+i}{2})$$

Divide -7+i by 2 to get -\frac{7}{2}+\frac{1}{2}i.

$$Re(-\frac{7}{2}+\frac{1}{2}i)$$

The real part of -\frac{7}{2}+\frac{1}{2}i is -\frac{7}{2}.

$$-\frac{7}{2}$$