Solve |+i/2+bi=1/2i

$$\frac { | + i } { 2 + b i } = \frac { 1 } { 2 } i$$

Solve for b

$$b=-2+2i$$

Steps for Solving Linear Equation

Variable b cannot be equal to 2i since division by zero is not defined. Multiply both sides of the equation by ib+2.

$$|i|=\frac{1}{2}i\left(ib+2\right)$$

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of i is 1.

$$1=\frac{1}{2}i\left(ib+2\right)$$

Use the distributive property to multiply \frac{1}{2}i by ib+2.

$$1=-\frac{1}{2}b+i$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{1}{2}b+i=1$$

Subtract i from both sides.

$$-\frac{1}{2}b=1-i$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$b=\left(1-i\right)\left(-2\right)$$

Multiply 1-i and -2 to get -2+2i.

$$b=-2+2i$$