Solving task on-line

Complex numbers

For example, to simplify the expression

We write as (-1+2i)(3-4i)/(2+i) and click on the sign (=). See the section "Result".

Write a complex number in trigonometric form

z = -1 - 4i Basic formula: z = |z|[cos(φ+2πk) + i sin(φ+2πk)] где φ = arctg((-4)/(-1));
|z| = ((-1)² + (-4)²)^1/2

1. find angle φ. Write arg(-1-4i) and click on the sign (=). See the section "Exact result".
2. find module |z|. Write abs(-1-4i) and click on the sign (=). See the section "Exact result".

Write a complex number in exponential form

z = |z|e^iφ

Note: tan^-1 = arctg (arctangent of the angle). Example, φ = tan^-1(4) - π = arctg(4) - π

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