IB Mathematics Applications & Interpretation Question Type 2: Working with Conjugate of Complex Numbers Exercises

Let $z=x+yi$ satisfy $z+\bar{z}=10$. Find the value of $x$.

Simplify the expression $\frac{3+2i}{1-i}$ by rationalizing the denominator.

Compute the modulus of $5-12i$ by using its conjugate.

Simplify the expression $$\frac{1+2i}{3-4i}+\frac{5-i}{2+i}$$ and express the result in the form $a+bi$.

Multiply the complex number $4-3i$ by its conjugate and simplify the result.

Let $z=x+yi$. Show that $z\bar{z}=x^2+y^2$.

Solve for $z$ if $\bar{z}=2+3i$.

Find the conjugate of $-2+5i$ and then compute the product of the number with its conjugate.

Express $\frac{1}{1+i}$ in the form $a+bi$.

Find the conjugate of the complex number $4-3i$.

Simplify $\frac{2-3i}{4+i}$ and express your answer in the form $a+bi$.

Simplify $\frac{5+3i}{2+3i}$ and write your answer in the form $a+bi$.